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I need a book which explains the concepts of measure, set functions, outer meaures, extension of meaures, measurable functions, outer measurable functions and Lebesgue measure
kindly help me...

José Carlos Santos
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Bassam Hassan Khan
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  • Royden's Real Analysis comes to mind. –  Aug 20 '17 at 10:03
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    Try the book Measure and integration of Inder.K.Rana...it is suitable for begginers..And contains everything you mention. – Marios Gretsas Aug 20 '17 at 10:04
  • Royden's book is not for begginers @G.Sassatelli. – Marios Gretsas Aug 20 '17 at 10:04
  • @MariosGretsas We might not agree on the meaning of "beginner". Certainly, the book does the things of measure theory around Carathéodory's theorem from scratch. Twice, actually: once for the Lebesgue measure on $\Bbb R^n$ and once for general measures. –  Aug 20 '17 at 10:08
  • @G.Sassatelli Royden's book is perfect in general....in my opinion a begginer in measure theory is one that has not even seen lebesgue measure and integral or has started from these forst..I believe the best way to start learning measure theory is to firstly learn the consept of lebesgue measure and integral and then continue..I dont know if you agree with me but indeed the book you proposed is great just not for the O.P for now i believe.. – Marios Gretsas Aug 20 '17 at 10:18
  • For instance the O.P can start with lecture note or a book in lebesgue measure and then go to more advanced books..For me ,a begginer to start in measure theory with abstract measure spaces and measures,extensions theorems,,radon measures etc is like hunting a lion with a slingshot..(im not refering on Royden's book or the above coment of Sassatelli off course, i just expresed a general belief of mine). – Marios Gretsas Aug 20 '17 at 10:20

4 Answers4

7

I suggest Measure theory, by Donald L. Cohn.

José Carlos Santos
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I'm surprised that no one mentionned the famous Rudin's book : Real and Complex Analysis. As a student, it really helped me. Moreover, at the end of each chapter there is an historical note on the subject we just studied. Really interesting and helpful.

Sov
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Here are $\textbf{3}$.

$\bullet$ Real analysis for graduate students by Richard F. Bass

$\bullet$ Royden, $3$rd or $4$th

$\bullet$ M.T (https://www.ndsu.edu/pubweb/~comez/Lecture%20Notes%20and%20Talks.htm)

The second are notes from a professor at my university. They worked really well for me when studying for my qualifying exams. I provided the first reading because it goes into more detail and has a similar style. The middle I used a lot as well. Most measure theory notes that you will find, if free, differ by a very small amount. So almost every set will have everything you need, its just a matter of finding the right style.

Faraad Armwood
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3

I would like to suggest three books which helped me-

1) Royden's Real Analysis,here in this it gives motivation towards the topic as well as illustrative text,nice examples,excercises.

2)Measure Theory and Integration by G. de Barra.

3)Paul Halmos,Measure theory.

Also there are some similar questions asked and may contain some references as per your requirement - Reference book on measure theory and here.

And some online notes here and here.

Hope this helps!

BAYMAX
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