Difference between revisions of "User:Boris Tsirelson/sandbox2"
From Encyclopedia of Mathematics
| Line 2: | Line 2: | ||
| − | 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]]; its | + | 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]]; its σ-algebra consists of all subsets, and its measure is the ''counting measure'' $\mu$: $\mu(A)$ is the number of points in $A$ ($\infty$ if $A$ is infinite). |
Revision as of 17:43, 21 July 2012
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; its σ-algebra consists of all subsets, and its measure is the counting measure $\mu$: $\mu(A)$ is the number of points in $A$ ($\infty$ if $A$ is infinite).
How to Cite This Entry:
Boris Tsirelson/sandbox2. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Boris_Tsirelson/sandbox2&oldid=27153
Boris Tsirelson/sandbox2. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Boris_Tsirelson/sandbox2&oldid=27153