I am looking for a comprehensive book on Probability which discusses Convergence of Random Variables in detail, excluding portions of Measure Theory. Allan Gut's "Probability: A Graduate Course" seems fabulous, but it has way too much content on Measure Theory, which I do not know at all.


There is a wealth of professors and undergrad students of Stats and Maths on this website; and I would like to directly ask you: which book should suit my situation? Because I CAN learn Measure Theory but considering I am only a first year undergrad, and Measure Theory will be taught to me three years later, I suppose it will only be a wastage of time.



Book on Convergence Concepts in Probability without Measure Theory
Grimmett and Stirzaker's Probability and Random Processes fits the bill:


[http://www.amazon.com/Probability-Random-Processes-Geoffrey-Grimmett/dp/0198572220](http://rads.stackoverflow.com/amzn/click/0198572220)


It covers everything up to stochastic calculus without measure theory. 


