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Putnam 1972 A3

Source: Putnam 1972

February 17, 2022
PutnamSequenceslimit

Problem Statement

A sequence (xi)(x_{i}) is said to have a Cesaro limit exactly if lim⁡n→∞x1+…+xnn\lim_{n\to\infty} \frac{x_{1}+\ldots+x_{n}}{n} exists. Find all real-valued functions ff on the closed interval [0,1][0, 1] such that (f(xi))(f(x_i)) has a Cesaro limit if and only if (xi)(x_i) has a Cesaro limit.
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