Lebesgue Measure & Integration by P.K Jain & V.K Gupta

Lebesgue Measure and Integration Jain, P.K. , Emeritus Fellow-UGC, Formerly, Prof. and Head, Deptt. of Math., University of Delhi, Delhi, India. Gupta, Ved Prakash , Prof. (Retired), National Council of Education Research & Training, New Delhi, India. Jain, Pankaj , Associate Prof., Deptt. of Mathematics, Deshbandhu College, (University of Delhi), New Delhi, India.

About the Book: The book is intended to provide a basic course in Lebesgue Measure and Integration for the Honours and Postgraduate students of the various universities in India and abroad with the hope that it will open a path to the Lebesgue Theory to the students. Pains have been taken to give detailed explanations of reasons of work and of the method used together with numerous examples and counter examples at different places in this book. The details are explicitly presented keeping the interest of the students in view. Each topic, in the book, has been treated in an easy and lucid style. The material has been arranged by sections, spread out in seven chapters. The text opens with a chapter on preliminaries discussing basic concepts and results which would be taken for granted later in the book. The chapter is followed by chapters on Infinite Sets, Measurable Sets, Measurable Functions, Lebesgue Integral, Differentiation and Integration and the Lebesgue Lp-Spaces. The book contains many solved and unsolved problems, remarks and notes at places which would help the students in learning the course effectively.

Measure Theory and Integration (First Edition) Michael E. Taylor

Measure Theory and Integration (First Edition) Michael E. Taylor 2012; 319 pp; Paperback; 180 × 240 mm; 978-0-8218-8718-9 For sale only in India,Nepal,Bhutan,Bangladesh,Sri Lanka,Maldives,Pakistan 720.00

Measure Theory And Probability by A. K. Basu

 Price  Rs 225/=

Book Summary of Measure Theory And Probability

This compact and wellreceived book, now in its second edition, is a skilful combination of measure theory and probability. For, in contrast to many books where probability theory is usually developed after a thorough exposure to the theory and techniques of measure and integration, this text develops the Lebesgue theory of measure and integration, using probability theory as the motivating force.

What distinguishes the text is the illustration of all theorems by examples and applications. A section on Stieltjes integration assists the student in understanding the later text better.

For easy understanding and presentation, this edition has split some long chapters into smaller ones. For example, old Chapter 3 has been split into Chapters 3 and 9, and old Chapter 11 has been split into Chapters 11, 12 and 13.

The book is intended for the firstyear postgraduate students for their courses in Statistics and Mathematics (pure and applied), computer science, and electrical and industrial engineering.

KEY FEATURES :

Measure theory and probability are well integrated.

Exercises are given at the end of each chapter, with solutions provided separately.

A section is devoted to large sample theory of statistics, and another to large deviation theory (in the Appendix).

About the Author
(Late) A.K. BASU, PhD, was formerly faculty in the Department of Statistics, Calcutta University. His various assignments saw him serving at the University of Illinois (Chicago), University of Brasilia (Brazil), and the Laurentian University (Canada). Besides, he was a Visiting Faculty at the University of Regina, McMaster, and Ottawa (all in Canada); IPN (Mexico); and the Indian Statistical Institute, Calcutta.

Dr. Basu was a member of the Institute of Mathematical Statistics, International Statistical Association, and the Statistical Science Association of Canada. He published several articles in reputed national and international journals.

Table of Contents
Editor’s Preface Preface to the First Edition List of Symbols and Abbreviations
1. Introduction: Sets, Indicator Functions, and Classes of Sets
2. Measure Space and Probability Space
Distribution Functions
4. Measurable Functions
5. Integration Theory and Expectation
6. Types of Convergence and Limit Theorems
7. Independence
8. Law of Large Numbers and Associated Limit Theorems
9. Characteristic Functions
10. Central Limit Theorem (CLT)
11. Product Space
12. Conditional Expectation
13. Martingale
14. Measure Extension and LebesgueStieltjes Measure
Appendix I Measure on Infinite Product Space and Kolmogorov’s Consistency
Appendix II HahnJordan Decomposition
Appendix III Large Sample Theory References
Author Index
Subject Index

Details of Book: Measure Theory And Probability

Book:	Measure Theory And Probability
Author:	A. K. Basu
ISBN:	8120343859
ISBN-13:	9788120343856 ,  978-8120343856
Publishing Date:	2012
Publisher:	PHI LEARNING PVT. LTD-NEW DELHI
Edition:	2ndEdition
Number of Pages:	240