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We now introduce our abstraction for a “class of mathematical questions” (with quantitative real-valued answers). This abstraction is a trivial generalization of the concept of a distributional decision problem from average-case complexity theory (see e.g. \cite{Bogdanov_2006}).

A distributional estimation problem is a pair \((\mu,f)\) where \(\mu\) is a word ensemble and \(f: \operatorname{supp}\mu \rightarrow {\mathbb{R}}\) is bounded.