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Large deviations type results for sum of i.i.d. random functions

Assume that $f_1, f_2, f_3,\ldots$ are i.i.d. random functions $[0,1]\mapsto \mathbb{R}$ such that (1) random variables $M_k=\sup_{x\in[0,1]}f_k(x)$ have exponential tails, (2) $f$'s are a.s. Lipsch …
Serguei Popov's user avatar