Suppose that we are given a sequence of continuous functions $f_n$ which are non-negative, integrate to $1$ and supported on intervals $[-x_n,x_n]$ with $\sum_{n \geq 1} x_n$ converging where $x_n \geq 0$ for every $n$. If we set $F_n;=f_1 *\cdots *f_n$, where $*$ denotes convolution, is it true that $\lim_{n \to \infty} F_n$ is differentiable?
2026-04-11 10:53:03.1775904783
Derivative of a limit
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