= Solution
For disjoint nonempty <vertex> sets $X,Y$, let $e(X,Y)$ count edges with one endpoint in each. Their <edge density of a bipartite graph>[density] is
$$
\boxed{d(X,Y)=\frac{e(X,Y)}{|X||Y|}.}
$$
For $0<\epsilon<1$, the pair is a <regular pair of vertex sets> if all $X'\subseteq X$ and $Y'\subseteq Y$ with $|X'|\geq\epsilon|X|$ and $|Y'|\geq\epsilon|Y|$ satisfy
$$
\boxed{|d(X',Y')-d(X,Y)|\leq\epsilon.}
$$
Using the convention with a strict bound less than $\epsilon$ instead gives the same argument below; the assumed density is strictly larger than $\epsilon$.
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