I am not a math student, but I have taken courses in Calculus, Vector Algebra, Fourier and Laplace transforms, linear Algebra, elementary probability and stats while pursuing CompSci.

I work as a risk analyst and passed my CFA level II. I want to prep for a masters in financial engineering, which I intend to pursue in 2017. My current math background is as follows:

1) Read and solved all problems of Differential and Integral calculus by N. Piskunov.

2) Read the first six chapters of Principles of Mathematical Analysis by Walter Rudin.

3) Currently reading an introduction to probability by Blitzstein.

I would like to build a strong understanding of probability theory, martingales, real analysis and measure theory, before I get into the course. Given my background, what are few good books to pick up and solve, to learn measure theory(real analysis), which begin from the absolute basics. I am going to burn midnight oil... What would be the pre-requisites.

I am sorry, if my thread overlaps with other similar posts. I did search through the other posts.

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    $\begingroup$ To start with, finish Chapter 7 of PMA. $\endgroup$ – Qiyu Wen Jul 22 '16 at 4:26
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    $\begingroup$ Tao has a free book terrytao.files.wordpress.com/2011/01/measure-book1.pdf $\endgroup$ – n1000 Jul 22 '16 at 4:36
  • $\begingroup$ Chapter 11 of PMA / chapter 1 of RCA are pretty straightforward and good for an introduction, IMO $\endgroup$ – MCT Jul 22 '16 at 4:58
  • $\begingroup$ @MichaelTong, what would be a good next step, Rudin's RCA, or would there be an intermediary book, perhaps? $\endgroup$ – Quasar Jul 22 '16 at 5:03
  • $\begingroup$ Rudin's RCA starts off with a very abstract construction of the Lebesgue integral. Whether or not it's right for you really depends on your background and taste, I think. If you prefer something more concrete, there are many books that would probably be better choices, e.g. Royden. $\endgroup$ – solstafir Jul 22 '16 at 5:11

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