I am looking for an advice on a good textbook in measure and
probability. Most graduate level textbooks that I have seen just lay
out definitions and theorems and do not give any intuition behind those
definitions. I am looking for a textbook  that does more. For example,
I would like to see an intuitive explanation why such transformation of
a random variable as an expectation may be representative, and why in
applied statistical models we may concentrate on expectations; and I
want an explanation built on arguments other than law of large numbers.



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