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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

2 votes

Function is almost everywhere 1 w.r.t. sequence of regular Borel probability measures

The statement you want to prove seems wrong: for instance on $K=[0,1]$ with $U=]0,1[$ let $(q_n)$ be countable dense in $U$, and let $\mu_n$ be the Dirac measure on $q_n$. Because the measures are Dir …
François Le Maître's user avatar