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for questions involving inequalities, upper and lower bounds.

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Why does the assumption $|U_t| \le \frac1{p_{\min}}$ work in this paper?

I am reading a 2009 paper right now "Importance Weighted Active Learning" and on page 5, there is a theorem that uses the inequality $|U_t| \leq \frac{1}{p_{\min}}$. I am not sure how the paper found …
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