On the average value of a function of generalized mean
Abstract
In this short note we find the exact formula for
$$\lim_{n\rightarrow\infty}\idotsint_{[0,1]^n}f(M_{n,p}(x_1,\dots, x_n))\,dx_1\dots dx_n,$$
where $M_{n,p}(x_1,\dots, x_n)$, $p\in [-\infty,\infty]$ is the generalized mean and $f$ is an arbitrary continuous function.
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