Suppose that I have the following situation: everything takes place on complex plane, I have some probabilistic measure $\mu$ and suppose that I have a family of function $(u_w)_w$ parametrised by $w$ where $w$ runs throught some subset of the complex plane (it may be whole $\mathbb{C}$). Suppose that all $u_w$'s are integrable with respect to the standard flat Lebesgue measure $dxdy$. Is it true that almost (with respect to $dxdy$) all $u_w$'s are $\mu$ integrable? How to prove this?
2026-05-06 07:21:55.1778052115
Changing the measure
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