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Putnam 2012 A6

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December 3, 2012
Putnamfunctioncalculusintegrationrectanglecollege contestsreal analysis

Problem Statement

Let f(x,y)f(x,y) be a continuous, real-valued function on R2.\mathbb{R}^2. Suppose that, for every rectangular region RR of area 1,1, the double integral of f(x,y)f(x,y) over RR equals 0.0. Must f(x,y)f(x,y) be identically 0?0?
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