Re: Question about Lebesque Integral

On 3 May 2005 14:37:47 -0700, agapito6314@xxxxxxx wrote:

>The Lebesque integral ,I, of function f with respect to measure u is
>defined by
>
>I (f du) = I (f+ du) - I (f- du)
>
>where f+ and f- are the positive and negative parts of f, respectively.
> Now my text (Bartle) states that "it is easy to see that if" f = v -
>w, with v and w non-negative, then
>
>I (f du)= I (v du) - I ( w du)
>
>I don't see how this follows from the basic definition of I as supremum
>of integrals of simple functions. Can someone please help with a proof?

You got several replies the first time you posted this question.

> Thanks.


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David C. Ullrich
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