Lebesgue Measure and Integration PK Jain 9788122431193 Books
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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.
Lebesgue Measure and Integration PK Jain 9788122431193 Books
One of the best book I ever seen. Not perfect since misses some explanations but anywhere very nice bookProduct details
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Tags : Lebesgue Measure and Integration [P.K. Jain] on Amazon.com. *FREE* shipping on qualifying offers. 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,P.K. Jain,Lebesgue Measure and Integration,New Age International Pvt. Ltd.,8122431194,Nonfiction
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Lebesgue Measure and Integration PK Jain 9788122431193 Books Reviews
For starters, this book uses non-standard notations or standard notations with non-standard meaning, which is annoying. For example, the bold capital letter I is used to denote of set of integers (rather than the standard Z). The standard blackboard bold letter N is used for the set of natural numbers, but the author excludes zero from that set (the author actually never defines N but it's apparent that zero is excluded from the given examples.) There are also quite a few typos (to cite just one example on page 20 "In the binary system every natural number x can be uniquely represented by x=sum from n=1 to infinity of x_n / 2^(n-1), where x_n is either 0 or 1."), but I gave up on the book when it claimed that the continuum hypothesis (the question of whether there exists a cardinal number strictly between the cardinality of the integers and the cardinality of the real numbers) was still an unsolved problem! ("This problem is yet unsolved").
For some strange reason, the author also develops the theory of cardinal numbers, which is only very marginally relevant to Lebesgue measure and integration. Sure, it's an interesting topic, but it really distracts from the main topic, and does not really belong in such a book.
The book has some redeeming features. In Appendix III, it has the English translation of Henri Lebesgue's lecture called "The Development of the Notion of the Integral" (reproduced from the book "Lebesgue Integration", by Soo Bong Chae, Marcel Dekker, New York, No. 58 (1980)). This lecture is a masterpiece.
It is also written in an accessible manner with good examples, definitions and theorems clearly stated, and instructive discussions, and a fair number of exercises.
However, these positive qualities are more than offset by the aforementioned flaws.
This book is one of the best books ever written on this subject .There are lots of worked out problems (something lacking in most books), and the theorems are fully proved.Lebesgue theory is a very hard subject to learn, and this book makes the learning easier because of the author's desire to reach out.A big danger in trying to learn a subject like Lebesgue measure and integration is that it is easy to learn how to push the symbols on a peice of paper without really understanding what is going on.This book tries to develop the reader's intuition and the ideas behind the symbols. This book is much better than all current textbooks used at American Universities.A great book overall.
The book arrived on time in excellent condition.
It is a good introduction to mathematical measure theory.
It was used in a UCLA extension class on measure theory winter 2014
One of the best book I ever seen. Not perfect since misses some explanations but anywhere very nice book
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