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Putnam 1968 B4

Source: Putnam 1968

February 19, 2022
PutnamintegrationMeasure theory

Problem Statement

Suppose that f:R→Rf:\mathbb{R} \rightarrow \mathbb{R} is continuous and L=∫−∞∞f(x)dxL=\int_{-\infty}^{\infty} f(x) dx exists. Show that ∫−∞∞f(x−1x)dx=L.\int_{-\infty}^{\infty}f\left(x-\frac{1}{x}\right)dx=L.
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