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 f:X→R on a measurable space (X,A) is a[1]:
- function of the form ∑Ni=1xi1Ai(x) for
- finitely many sets, A1,…,AN∈A and
- finitely many x1,…,xn∈R
