Difference between revisions of "User:Boris Tsirelson/sandbox2"
From Encyclopedia of Mathematics
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| − | 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]]; | + | 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 $a:\{0,1,2,\dots\}\to\R$ |
Revision as of 17:47, 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; 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 $a:\{0,1,2,\dots\}\to\R$
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