| Line 3: | Line 3: | ||
<math>\lambda(B)=\frac{\mu(B)}{\mu(A)}</math> | <math>\lambda(B)=\frac{\mu(B)}{\mu(A)}</math> | ||
| − | 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 \frac{}{}</math> |
Moreover, <math>\int_{A}fd\mu = \mu(A)\int_A f d\lambda \frac{}{}</math> | Moreover, <math>\int_{A}fd\mu = \mu(A)\int_A f d\lambda \frac{}{}</math> | ||
Revision as of 09:47, 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 \frac{}{} $
Moreover, $ \int_{A}fd\mu = \mu(A)\int_A f d\lambda \frac{}{} $
