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This is clearly a measure on <math>A</math> with <math>\lambda(A)=1</math> | This is clearly a measure on <math>A</math> with <math>\lambda(A)=1</math> | ||
| − | Moreover, <math>\int_{A}fd\mu = \mu(A)\int_A f d\lambda</math> | + | Moreover, <math>\int_{A}fd\mu = \mu(A)\int_A f d\lambda \frac{}{}</math> |
Revision as of 09:46, 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 \frac{}{} $
