I am having Measure Theory as a subject in my course.It is having these as topics:
1.Lebesgue measure on the line
2.Measurable functions
3.Lebesgue integral
4.Convergence almost everywhere
5.Monotone and dominated convergence theorems
I searched for many books on the web but cant figure out which one to start with.can someone please help me by recommending a book which covers the above topics and also has some standard exercises to work on.Thanks
On
The cheapest option I can think of is Richard Bass' Book. It's a fairly concise read, but it covers all of the major topics you mentioned and also the formal relationship between Lebesgue integration and measure theory to probability. Another really great read is G.F. Simmons' Book which covers more on operator theory later on in the text. I'd also recommend Lieb and Loss, but this might be a more advanced read for a first pass at Lebesgue theory. One thing I ought to mention is that Bass' book doesn't cover Hilbert spaces, which may not be so bad for a first course, but it won't be sufficient later on.
Rudin's "Principles of Math Analysis" is classic...