The BEST book of measure theory for beginners 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...
 A: I suggest Measure theory, by Donald L. Cohn.
A: 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.
A: 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. 
A: 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! 
