- **Real Analysis**
(*http://mymathforum.com/real-analysis/*)

- - **Lebesgue integration question**
(*http://mymathforum.com/real-analysis/41654-lebesgue-integration-question.html*)

Lebesgue integration questionLebesgue integral question: Consider measure space with a summable function. I want to show that if then a.e. and therefore a.e. My proposed proof is as follows: Assume that for some . Since is positive measurable function it follows that it is the limit of an increasing sequence of simple functions which I will show as : Using Beppoi Levi I know that the limit of the integral is the integral of the limit which gives the following: This is only possible if for any we have . for all and it follows that either or . Since we assumed that is nonzero for some it follows that there is some where therefore there must be some such that and which gives for . It follows that a.e. and therefore a.e. Is this proof fine? Thanks for assistance. |

All times are GMT -8. The time now is 01:20 PM. |

Copyright © 2019 My Math Forum. All rights reserved.