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I am still a freshmen taking statistics and am disappointed with a second semester statistical theory course which just raves on from typical distributions to bi-variate random variables to random variable functions and Order Statistics.

I am mad with my teacher who pretty much expects the class to "remember" he theories and fails to explain their origin or source.

Although I am yet to learn Analysis or collegiate integral calculus for that matter I found this book "An Outline of Statistical Theory - Goon, Gupta, Dasgupta" which teaches probability from a measure theoretic perspective and am enjoying it. Although I don't get concepts like the Lebesgue-Stieltjes integral, I am however enjoying the rigor and the grassroot teaching of the book.

Looking for books on measure theory/ Probability that might further help me understand statistics properly instead of superficially. Any suggestions will be greatly appreciated..

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To understand statistics from the very grassroots, I think the book Statistics, 4th edition by Freedman, Purves, Pisani will be very appropriate. The most basic book on Probability is An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd Edition by Feller. And you are telling me that you are not also sure about Lebesgue-Stieltjes Integral. You have to strengthen your Real Analysis skills very much before you should start Measure theory. A very good book on Real Analysis is Real Mathematical Analysis by Charles C. Pugh. This book also includes basic Measure thoery.

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