The Theory of Lebesgue Measure and Integration deals with the theory of Lebesgue measure and integration and introduces the reader to the theory of real functions. The subject matter comprises concepts and theorems that are now considered classical, including the Yegorov, Vitali, and Fubini theorems. The Lebesgue measure of linear sets is discussed, along with measurable functions and the definite Lebesgue integral. Comprised of 13 chapters, this volume begins with an overview of basic concepts such as set theory, the denumerability and non-denumerability of sets, and open sets and closed sets on the real line. The discussion then turns to the theory of Lebesgue measure of linear sets based on the method of M. Riesz, together with the fundamental properties of measurable functions. The Lebesgue integral is considered for both bounded functions — upper and lower integrals — and unbounded functions. Later chapters cover such topics as the Yegorov, Vitali, and Fubini theorems; convergence in measure and equi-integrability; integration and differentiation; and absolutely continuous functions. Multiple integrals and the Stieltjes integral are also examined. This book will be of interest to mathematicians and students taking pure and applied mathematics.

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Yes, you can access The Theory of Lebesgue Measure and Integration by S. Hartman,J. Mikusinski, I. N. Sneddon,M. Stark,S. Ulam in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over one million books available in our catalogue for you to explore.

Information

Publisher

Pergamon

Year

2014

ISBN

9781483280332

Topic

Mathematics

Subtopic

Mathematics General

Index

Mathematics

Front Cover
The Theory of Lebesgue Measure and Integration
Copyright Page
Table of Contents
Foreword to the English Edition
CHAPTER I. INTRODUCTORY CONCEPTS
CHAPTER II. LEBESGUE MEASURE OF LINEAR SETS
CHAPTER III. MEASURABLE FUNCTIONS
CHAPTER IV. THE DEFINITE LEBESGUE INTEGRAL
CHAPTER V. CONVERGENCE IN MEASURE AND EQUI-INTEGRABILITY
CHAPTER VI. INTEGRATION AND DIFFERENTIATION FUNCTIONS OF FINITE VARIATION
CHAPTER VII. ABSOLUTELY CONTINUOUS FUNCTIONS
CHAPTER VIII. SPACES OF p-th POWER INTEGRABLE FUNCTIONS
CHAPTER IX. ORTHOGONAL EXPANSIONS
CHAPTER X. COMPLEX-VALUED FUNCTIONS OF A REAL VARIABLE
CHAPTER XI. MEASURE IN THE PLANE AND IN SPACE
CHAPTER XII. MULTIPLE INTEGRALS
CHAPTER XIII. THE STIELTJES INTEGRAL
Literature
Index