اندازه‌گیری و انتگرال

Probability and Mathematical Statistics: Measure and Integral provides information pertinent to the general mathematical notions and notations. This book discusses how the machinery of ?-extension works and how ?-content is derived from ?-measure. Organized into 16 chapters, this book begins with an overview of the classical Hahn–Banach theorem and introduces the Banach limits in the form of a major exercise. This text then presents the Daniell extension theory for positive ?-measures. Other chapters consider the transform of ?-contents and ?-measures by measurable mappings and kernels. This text is also devoted to a thorough study of the vector lattice of signed contents. This book discusses as well an abstract regularity theory and applied to the standard cases of compact, locally compact, and Polish spaces. The final chapter deals with the rudiments of the Krein–Milman theorem, along with some of their applications. This book is a valuable resource for graduate students. Content: Front Matter, Page iii Copyright, Page iv PREFACE, Pages ix-xv CHAPTER 0 - BASIC NOTIONS AND NOTATION, Pages 1-25 CHAPTER I - POSITIVE CONTENTS AND MEASURES, Pages 26-71 CHAPTER II - EXTENSION OF σ-CONTENTS AFTER CARATHÉODORY, Pages 72-87 CHAPTER III - EXTENSION OF POSITIVE σ- AND τ-MEASURES, AFTER DANIELL, Pages 88-147 CHAPTER IV - TRANSFORM OF σ-CONTENTS, Pages 148-195 CHAPTER V - CONTENTS AND MEASURES IN TOPOLOGICAL SPACES. PART I: REGULARITY, Pages 196-211 CHAPTER VI - CONTENTS AND MEASURES IN PRODUCT SPACES, Pages 212-264 CHAPTER VII - SET FUNCTIONS IN GENERAL, Pages 265-281 CHAPTER VIII - THE VECTOR LATTICE OF SIGNED CONTENTS, Pages 282-324 CHAPTER IX - THE VECTOR LATTICE OF SIGNED MEASURES, Pages 325-343 CHAPTER X - THE SPACES Lp, Pages 344-356 CHAPTER XI - CONTENTS AND MEASURES IN TOPOLOGICAL SPACES. PART II: THE WEAK TOPOLOGY, Pages 357-373 CHAPTER XII - THE HAAR MEASURE ON LOCALLY COMPACT GROUPS, Pages 374-401 CHAPTER XIII - SOUSLIN SETS, ANALYTIC SETS, AND CAPACITIES, Pages 402-435 CHAPTER XIV - ATOMS, CONDITIONAL ATOMS, AND ENTROPY, Pages 436-456 CHAPTER XV - CONVEX COMPACT SETS AND THEIR EXTREMAL POINTS, Pages 457-483 CHAPTER XVI - LIFTING, Pages 484-513 APPENDIX A - THE PERRON–WARD INTEGRAL AND RELATED CONCEPTS, Pages 515-533 APPENDIX B - CONTENTS WITH GIVEN MARGINALS, Pages 534-548 SELECTED BIBLIOGRAPHY, Pages 549-560 INDEX, Pages 561-575 Probability and Mathematical Statistics: A Series of Monographs and Textbooks, Page ibc1