User:Boris Tsirelson/sandbox2

Relations to Lebesgue integral

It is possible to treat absolutely convergent series as a special case of Lebesgue integrals. To this end, the countable set $\{0,1,2,\dots\}$ is treated as a measure space; all subsets are measurable, and the counting measure $\mu$ is used: $\mu(A)$ is the number of points in $A$ ($\infty$ if $A$ is infinite). A sequence $(a_n)_n$ is a function $a:\{0,1,2,\dots\}\to\R$