MathDB

Suppose that

f: \mathbb R^2\rightarrow \mathbb R

is a non-negative and continuous function that \iint_{\mathbb R^2}f(x,y)dxdy\equal{}1. Prove that there is a closed disc

D

with the least radius possible such that \iint_D f(x,y)dxdy\equal{}\frac12.

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