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## Traian Lalescu student contest 2011 Problem 3

For a continuous function $f : [0,\infty) \to [0,\infty)$ such that $\displaystyle \int_0^\infty f(x)dx <\infty$ prove that if $f$ is uniformly continuous, then it is bounded. Prove also that the converse of the previous statement is not true.

Traian Lalescu student contest 2011