Putnam 2012 A6

Session A

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

Curated text Kedlaya Putnam archive. Quoted with source.

Solutions

Human solution Solution 1 by Kiran Kedlaya and Lenny Ng

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