Simple function (measure theory)/Definition
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Revision as of 07:16, 12 March 2016 by Alec (Talk | contribs) (Created page with "<noinclude> ==Definition== </noinclude> A ''simple function'' {{M|f:X\rightarrow\mathbb{R} }} on a measurable space {{M|(X,\mathcal{A})}} is a{{rMIAMRLS}}: * function of t...")
Definition
A simple function [ilmath]f:X\rightarrow\mathbb{R} [/ilmath] on a measurable space [ilmath](X,\mathcal{A})[/ilmath] is a[1]:
- function of the form [ilmath]\sum^N_{i=1}x_i\mathbf{1}_{A_i}(x)[/ilmath] for
- finitely many sets, [ilmath]A_1,\ldots,A_N\in\mathcal{A} [/ilmath] and
- finitely many [ilmath]x_1,\ldots,x_n\in\mathbb{R} [/ilmath]
