Simple function (measure theory)
From Maths
Revision as of 05:42, 12 March 2016 by Alec (Talk | contribs) (Created page with "{{Stub page|Needs fleshing out}} {{Todo|Cross reference with Halmos' book}} __TOC__ ==Definition== A ''simple function'' {{M|f:X\rightarrow\mathbb{R} }} on a measurable spac...")
(Unknown grade)
This page is a stub
This page is a stub, so it contains little or minimal information and is on a to-do list for being expanded.The message provided is:
Needs fleshing out
TODO: Cross reference with Halmos' book
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]
Standard representation
Standard representation (measure theory)/Definition
References
| ||||||||||||||||||||
