Basic Analysis I — Real Analysis · Problem 6.2.3

Sequences of Functions — Jiri Lebl

Mathematics — Real Analysis · limit-of-integral

Problem

Let f:[0,1]→Rf : [0, 1] \to \mathbb{R} be Riemann integrable (hence bounded). Find lim⁡n→∞∫01f(x)n dx\displaystyle\lim_{n \to \infty} \int_0^1 \frac{f(x)}{n}\, dx.

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