Question 66
Show that, if $f: [0, 1] \to [0, 1]$ is an integrable function, then
$$
\lim_{n \to \infty} n \int_{0}^{1} (f(x))^{n} (1 - f(x)) \, dx = 0.
$$
$$
\lim_{n \to \infty} n \int_{0}^{1} (f(x))^{n} (1 - f(x)) \, dx = 0.
$$
MathNet 2017-part-05 — 176 problems (EN–VI) Question 66
Math Olympiad Vault · MathNet 2017-part-05 — 176 problems (EN–VI)