Analytic Inequalities / Pachpatte, B.G (2012)  

Público ISBD Título : Analytic Inequalities : Recent Advances Tipo de documento: documento electrónico Autores: Pachpatte, B.G ; SpringerLink (Online service) Editorial: Paris : Atlantis Press Fecha de publicación: 2012 Colección: Atlantis Studies in Mathematics, ISSN 1875-7634 num. 3 Número de páginas: X, 306 p Il.: online resource ISBN/ISSN/DL: 978-94-91216-44-2 Idioma : Inglés (eng) Palabras clave: Mathematics  Functions  of  real  variables  Real Clasificación: 51 Matemáticas Resumen: For more than a century, the study of various types of inequalities has been the focus of great attention by many researchers, interested both in the theory and its applications. In particular, there exists a very rich literature related to the well known Cebysev, Gruss, Trapezoid, Ostrowski, Hadamard and Jensen type inequalities. The present monograph is an attempt to organize recent progress related to the above inequalities, which we hope will widen the scope of their applications. The field to be covered is extremely wide and it is impossible to treat all of these here. The material included in the monograph is recent and hard to find in other books. It is accessible to any reader with a reasonable background in real analysis and an acquaintance with its related areas. All results are presented in an elementary way and the book could also serve as a textbook for an advanced graduate course. The book deserves a warm welcome to those who wish to learn the subject and it will also be most valuable as a source of reference in the field. It will be invaluable reading for mathematicians and engineers and also for graduate students, scientists and scholars wishing to keep abreast of this important area of research Nota de contenido: Grüss- and Cebyšev-type inequalities -- Multidimensional Grüss-Cebyšev and -Trapezoid-type inequalities -- Ostrowski-type inequalities -- Multidimensional Ostrowski-type inequalities -- Inequalities via convex functions En línea: http://dx.doi.org/10.2991/978-94-91216-44-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33063 Analytic Inequalities : Recent Advances [documento electrónico] / Pachpatte, B.G ; SpringerLink (Online service) . - Paris : Atlantis Press, 2012 . - X, 306 p : online resource. - (Atlantis Studies in Mathematics, ISSN 1875-7634; 3) . ISBN : 978-94-91216-44-2 Idioma : Inglés (eng) Palabras clave: Mathematics  Functions  of  real  variables  Real Clasificación: 51 Matemáticas Resumen: For more than a century, the study of various types of inequalities has been the focus of great attention by many researchers, interested both in the theory and its applications. In particular, there exists a very rich literature related to the well known Cebysev, Gruss, Trapezoid, Ostrowski, Hadamard and Jensen type inequalities. The present monograph is an attempt to organize recent progress related to the above inequalities, which we hope will widen the scope of their applications. The field to be covered is extremely wide and it is impossible to treat all of these here. The material included in the monograph is recent and hard to find in other books. It is accessible to any reader with a reasonable background in real analysis and an acquaintance with its related areas. All results are presented in an elementary way and the book could also serve as a textbook for an advanced graduate course. The book deserves a warm welcome to those who wish to learn the subject and it will also be most valuable as a source of reference in the field. It will be invaluable reading for mathematicians and engineers and also for graduate students, scientists and scholars wishing to keep abreast of this important area of research Nota de contenido: Grüss- and Cebyšev-type inequalities -- Multidimensional Grüss-Cebyšev and -Trapezoid-type inequalities -- Ostrowski-type inequalities -- Multidimensional Ostrowski-type inequalities -- Inequalities via convex functions En línea: http://dx.doi.org/10.2991/978-94-91216-44-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33063

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Topics in Measure Theory and Real Analysis / Kharazishvili, Alexander B (2009)  

Público ISBD Título : Topics in Measure Theory and Real Analysis Tipo de documento: documento electrónico Autores: Kharazishvili, Alexander B ; SpringerLink (Online service) Editorial: Paris : Atlantis Press Fecha de publicación: 2009 Colección: Atlantis Studies in Mathematics, ISSN 1875-7634 num. 2 Número de páginas: XI, 461 p Il.: online resource ISBN/ISSN/DL: 978-94-91216-36-7 Idioma : Inglés (eng) Palabras clave: Mathematics  Measure  theory  and  Integration Clasificación: 51 Matemáticas Resumen: This book highlights various topics on measure theory and vividly demonstrates that the different questions of this theory are closely connected with the central measure extension problem. Several important aspects of the measure extension problem are considered separately: set-theoretical, topological and algebraic. Also, various combinations (e.g., algebraic-topological) of these aspects are discussed by stressing their specific features. Several new methods are presented for solving the above mentioned problem in concrete situations. In particular, the following new results are obtained: the measure extension problem is completely solved for invariant or quasi-invariant measures on solvable uncountable groups; non-separable extensions of invariant measures are constructed by using their ergodic components; absolutely non-measurable additive functionals are constructed for certain classes of measures; the structure of algebraic sums of measure zero sets is investigated. The material presented in this book is essentially self-contained and is oriented towards a wide audience of mathematicians (including postgraduate students). New results and facts given in the book are based on (or closely connected with) traditional topics of set theory, measure theory and general topology such as: infinite combinatorics, Martin's Axiom and the Continuum Hypothesis, Luzin and Sierpinski sets, universal measure zero sets, theorems on the existence of measurable selectors, regularity properties of Borel measures on metric spaces, and so on. Essential information on these topics is also included in the text (primarily, in the form of Appendixes or Exercises), which enables potential readers to understand the proofs and follow the constructions in full details. This not only allows the book to be used as a monograph but also as a course of lectures for students whose interests lie in set theory, real analysis, measure theory and general topology Nota de contenido: The problem of extending partial functions -- Some aspects of the measure extension problem -- Invariant measures -- Quasi-invariant measures -- Measurability properties of real-valued functions -- Some properties of step-functions connected with extensions of measures -- Almost measurable real-valued functions -- Several facts from general topology -- Weakly metrically transitive measures and nonmeasurable sets -- Nonmeasurable subgroups of uncountable solvable groups -- Algebraic sums of measure zero sets -- The absolute nonmeasurability of Minkowski’s sum of certain universal measure zero sets -- Absolutely nonmeasurable additive Sierpi?ski-Zygmund functions -- Relatively measurable Sierpi?ski-Zygmund functions -- A nonseparable extension of the Lebesgue measure without new null-sets -- Metrical transitivity and nonseparable extensions of invariant measures -- Nonseparable left invariant measures on uncountable solvable groups -- Universally measurable additive functionals -- Some subsets of the Euclidean plane -- Restrictions of real-valued functions En línea: http://dx.doi.org/10.2991/978-94-91216-36-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34140 Topics in Measure Theory and Real Analysis [documento electrónico] / Kharazishvili, Alexander B ; SpringerLink (Online service) . - Paris : Atlantis Press, 2009 . - XI, 461 p : online resource. - (Atlantis Studies in Mathematics, ISSN 1875-7634; 2) . ISBN : 978-94-91216-36-7 Idioma : Inglés (eng) Palabras clave: Mathematics  Measure  theory  and  Integration Clasificación: 51 Matemáticas Resumen: This book highlights various topics on measure theory and vividly demonstrates that the different questions of this theory are closely connected with the central measure extension problem. Several important aspects of the measure extension problem are considered separately: set-theoretical, topological and algebraic. Also, various combinations (e.g., algebraic-topological) of these aspects are discussed by stressing their specific features. Several new methods are presented for solving the above mentioned problem in concrete situations. In particular, the following new results are obtained: the measure extension problem is completely solved for invariant or quasi-invariant measures on solvable uncountable groups; non-separable extensions of invariant measures are constructed by using their ergodic components; absolutely non-measurable additive functionals are constructed for certain classes of measures; the structure of algebraic sums of measure zero sets is investigated. The material presented in this book is essentially self-contained and is oriented towards a wide audience of mathematicians (including postgraduate students). New results and facts given in the book are based on (or closely connected with) traditional topics of set theory, measure theory and general topology such as: infinite combinatorics, Martin's Axiom and the Continuum Hypothesis, Luzin and Sierpinski sets, universal measure zero sets, theorems on the existence of measurable selectors, regularity properties of Borel measures on metric spaces, and so on. Essential information on these topics is also included in the text (primarily, in the form of Appendixes or Exercises), which enables potential readers to understand the proofs and follow the constructions in full details. This not only allows the book to be used as a monograph but also as a course of lectures for students whose interests lie in set theory, real analysis, measure theory and general topology Nota de contenido: The problem of extending partial functions -- Some aspects of the measure extension problem -- Invariant measures -- Quasi-invariant measures -- Measurability properties of real-valued functions -- Some properties of step-functions connected with extensions of measures -- Almost measurable real-valued functions -- Several facts from general topology -- Weakly metrically transitive measures and nonmeasurable sets -- Nonmeasurable subgroups of uncountable solvable groups -- Algebraic sums of measure zero sets -- The absolute nonmeasurability of Minkowski’s sum of certain universal measure zero sets -- Absolutely nonmeasurable additive Sierpi?ski-Zygmund functions -- Relatively measurable Sierpi?ski-Zygmund functions -- A nonseparable extension of the Lebesgue measure without new null-sets -- Metrical transitivity and nonseparable extensions of invariant measures -- Nonseparable left invariant measures on uncountable solvable groups -- Universally measurable additive functionals -- Some subsets of the Euclidean plane -- Restrictions of real-valued functions En línea: http://dx.doi.org/10.2991/978-94-91216-36-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34140

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Topological Groups and Related Structures / Alexander Arhangel’skii (2008)  

Público ISBD Título : Topological Groups and Related Structures Tipo de documento: documento electrónico Autores: Alexander Arhangel’skii ; SpringerLink (Online service) ; Tkachenko, Mikhail Editorial: Paris : Atlantis Press Fecha de publicación: 2008 Colección: Atlantis Studies in Mathematics, ISSN 1875-7634 num. 1 Número de páginas: XIV, 781p Il.: online resource ISBN/ISSN/DL: 978-94-91216-35-0 Idioma : Inglés (eng) Palabras clave: Mathematics  Group  theory  Algebraic  topology  Theory  and  Generalizations  Topology Clasificación: 51 Matemáticas Resumen: Algebraandtopology,thetwofundamentaldomainsofmathematics,playcomplem- tary roles. Topology studies continuity and convergence and provides a general framework to study the concept of a limit. Much of topology is devoted to handling in?nite sets and in?nity itself; the methods developed are qualitative and, in a certain sense, irrational. - gebra studies all kinds of operations and provides a basis for algorithms and calculations. Very often, the methods here are ?nitistic in nature. Because of this difference in nature, algebra and topology have a strong tendency to develop independently, not in direct contact with each other. However, in applications, in higher level domains of mathematics, such as functional analysis, dynamical systems, representation theory, and others, topology and algebra come in contact most naturally. Many of the most important objects of mathematics represent a blend of algebraic and of topologicalstructures. Topologicalfunctionspacesandlineartopologicalspacesingeneral, topological groups and topological ?elds, transformation groups, topological lattices are objects of this kind. Very often an algebraic structure and a topology come naturally together; this is the case when they are both determined by the nature of the elements of the set considered (a group of transformations is a typical example). The rules that describe the relationship between a topology and an algebraic operation are almost always transparentandnatural—theoperationhastobecontinuous,jointlyorseparately Nota de contenido: to Topological Groups and Semigroups -- Right Topological and Semitopological Groups -- Topological groups: Basic constructions -- Some Special Classes of Topological Groups -- Cardinal Invariants of Topological Groups -- Moscow Topological Groups and Completions of Groups -- Free Topological Groups -- R-Factorizable Topological Groups -- Compactness and its Generalizations in Topological Groups -- Actions of Topological Groups on Topological Spaces En línea: http://dx.doi.org/10.2991/978-94-91216-35-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34446 Topological Groups and Related Structures [documento electrónico] / Alexander Arhangel’skii ; SpringerLink (Online service) ; Tkachenko, Mikhail . - Paris : Atlantis Press, 2008 . - XIV, 781p : online resource. - (Atlantis Studies in Mathematics, ISSN 1875-7634; 1) . ISBN : 978-94-91216-35-0 Idioma : Inglés (eng) Palabras clave: Mathematics  Group  theory  Algebraic  topology  Theory  and  Generalizations  Topology Clasificación: 51 Matemáticas Resumen: Algebraandtopology,thetwofundamentaldomainsofmathematics,playcomplem- tary roles. Topology studies continuity and convergence and provides a general framework to study the concept of a limit. Much of topology is devoted to handling in?nite sets and in?nity itself; the methods developed are qualitative and, in a certain sense, irrational. - gebra studies all kinds of operations and provides a basis for algorithms and calculations. Very often, the methods here are ?nitistic in nature. Because of this difference in nature, algebra and topology have a strong tendency to develop independently, not in direct contact with each other. However, in applications, in higher level domains of mathematics, such as functional analysis, dynamical systems, representation theory, and others, topology and algebra come in contact most naturally. Many of the most important objects of mathematics represent a blend of algebraic and of topologicalstructures. Topologicalfunctionspacesandlineartopologicalspacesingeneral, topological groups and topological ?elds, transformation groups, topological lattices are objects of this kind. Very often an algebraic structure and a topology come naturally together; this is the case when they are both determined by the nature of the elements of the set considered (a group of transformations is a typical example). The rules that describe the relationship between a topology and an algebraic operation are almost always transparentandnatural—theoperationhastobecontinuous,jointlyorseparately Nota de contenido: to Topological Groups and Semigroups -- Right Topological and Semitopological Groups -- Topological groups: Basic constructions -- Some Special Classes of Topological Groups -- Cardinal Invariants of Topological Groups -- Moscow Topological Groups and Completions of Groups -- Free Topological Groups -- R-Factorizable Topological Groups -- Compactness and its Generalizations in Topological Groups -- Actions of Topological Groups on Topological Spaces En línea: http://dx.doi.org/10.2991/978-94-91216-35-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34446

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