$\displaystyle|\mathcal{F}|^k\leq \prod_{i\in I} |\mathcal{F}_i|^k$

That's a corollary to Shearer's Lemma, by the way.

(I haven't told you what $I$, $\mathcal{F}$ and $\mathcal{F}_i$ are; oh well)

Anyway. This is courtesy of Watch Math. It's pretty simple, in fact. And it'll make the math on this site prettier.

I may (read: probably won't) get around to rewriting all my math in $\color{white}\LaTeX$.

Edit: Hmm... it seems the LaTeX sometimes takes a little while to load properly. Please be patient.

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