(New page: Define a function from the set of all measurable subsets of <math>A</math> as below <math>\lambda(B)=\frac{\mu(B)}{\mu(A)}</math>) |
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| − | Define a function from the set of all measurable | + | Define a function from the set of all measurable subset <math>B</math> of <math>A</math> as below |
<math>\lambda(B)=\frac{\mu(B)}{\mu(A)}</math> | <math>\lambda(B)=\frac{\mu(B)}{\mu(A)}</math> | ||
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| + | This is clearly a measure on <math>A</math> with <math>\lambda(A)=1</math> | ||
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| + | Moreover, <math>\int_{A}fd\mu = \mu(A)\int_A f d\lambda</math> | ||
Revision as of 10:46, 22 July 2008
Define a function from the set of all measurable subset $ B $ of $ A $ as below
$ \lambda(B)=\frac{\mu(B)}{\mu(A)} $
This is clearly a measure on $ A $ with $ \lambda(A)=1 $
Moreover, $ \int_{A}fd\mu = \mu(A)\int_A f d\lambda $
