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Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.

2 votes
1 answer
534 views

Can the characteristic function of a Borel set be approached by a sequence of continuous fun...

Want to find $f_n$ a sequence of continuous functions, so that for all Borel regular measure $\mu$, we have $\int f_n d\mu\rightarrow\int \chi_\Delta d\mu$, as $n$ goes to infinity, where $\Delta$ i …