Difference between revisions of "Simple function (measure theory)"
From Maths
(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...") |
m |
||
| Line 2: | Line 2: | ||
{{Todo|Cross reference with Halmos' book}} | {{Todo|Cross reference with Halmos' book}} | ||
__TOC__ | __TOC__ | ||
| − | == | + | ==[[Simple function (measure theory)/Definition|Definition]]== |
| − | + | {{:Simple function (measure theory)/Definition}} | |
| − | + | ||
| − | + | ||
| − | + | ||
==[[Standard representation (measure theory)|Standard representation]]== | ==[[Standard representation (measure theory)|Standard representation]]== | ||
{{:Standard representation (measure theory)/Definition}} | {{:Standard representation (measure theory)/Definition}} | ||
Latest revision as of 07:16, 12 March 2016
(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
Contents
[hide]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
Standard representation
Standard representation (measure theory)/Definition
References
| ||||||||||||||||||||
