I have convinced myself of the following:

For every $(k,\epsilon^2\hspace{.005 in})$-strong extractor Ext, for every distribution $X$, if $\;\; k\leq$ $\:H_{\infty}$$(\hspace{.01 in}X\hspace{.015 in}) \;\;$ then the probability over the seed $U$ that the distribution of $\: \text{Ext}\hspace{.01 in}(\hspace{.01 in}X,U\hspace{.015 in}) \:$ is not $\epsilon$-close to uniform is at most $\epsilon$.

Are there any known explicit strong extractors that are known to handle seed reuse better than can be shown by using the above on a standard strong extractor?

What if each instance of "extractor" in the rest of this post was replaced with "blender"$\hspace{.01 in}$?


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