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THE EVOLU TION OF THE U N IFORM BOUNDEDNESS PRIN CIPLE (Received February 1989, revised May 1989) 1. Introduction A uniform boun
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![real analysis - Proving that if $X_n$ is uniformly bounded, and if $X = \lim_{n}X_n$ with probability 1, then $E[X] = \lim_{n} E[X_n]$? - Mathematics Stack Exchange](https://i.stack.imgur.com/fZKSs.png "real analysis - Proving that if $X_n$ is uniformly bounded, and if $X = \lim_{n}X_n$ with probability 1, then $E[X] = \lim_{n} E[X_n]$? - Mathematics Stack Exchange")
real analysis - Proving that if $X_n$ is uniformly bounded, and if $X = \lim_{n}X_n$ with probability 1, then $E[X] = \lim_{n} E[X_n]$? - Mathematics Stack Exchange
Lecture 2
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