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Counting measure

For $f:\mathbb N\to[0,\infty]$,
$$
\int_{\mathbb N}f\,d\#
=\sum_{n=1}^{\infty}f(n)
:=\sup_{F\subseteq\mathbb N\text{ finite}}\sum_{n\in F}f(n).
$$
A complex-valued function is integrable for counting measure exactly when its series is absolutely convergent.


Series as a Lebesgue integral against counting measure

Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 1 / 23H / c / Solution

Series as a Lebesgue integral against counting measure

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Series as a Lebesgue integral against counting measure

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