View source for Simple function (measure theory)

{{Stub page|Needs fleshing out}}
{{Todo|Cross reference with Halmos' book}}
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==Definition==
A ''simple function'' {{M|f:X\rightarrow\mathbb{R} }} on a [[measurable space]] {{M|(X,\mathcal{A})}} is a{{rMIAMRLS}}:
* function of the form {{M|1=\sum^N_{i=1}x_i\mathbf{1}_{A_i}(x)}} for
* finitely many sets, {{M|A_1,\ldots,A_N\in\mathcal{A} }} and
* finitely many {{M|x_1,\ldots,x_n\in\mathbb{R} }}
==[[Standard representation (measure theory)|Standard representation]]==
{{:Standard representation (measure theory)/Definition}}
==References==
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