Suppose that f is an integrable non-negative function mapping from a set X to all reals.

Let be disjoint sets in X, why is ?

Thanks.

Printable View

- Nov 9th 2009, 03:40 PMtttcomraderIntegrade with disjoint sets
Suppose that f is an integrable non-negative function mapping from a set X to all reals.

Let be disjoint sets in X, why is ?

Thanks. - Nov 9th 2009, 03:43 PMDrexel28
- Nov 10th 2009, 12:15 PMMoo
Oh yes he did at least several times :D

http://www.mathhelpforum.com/math-he...w-measure.html

http://www.mathhelpforum.com/math-he...rsections.html

http://www.mathhelpforum.com/math-he...t-algebra.html

http://www.mathhelpforum.com/math-he...open-sets.html

http://www.mathhelpforum.com/math-he...-infinity.html

http://www.mathhelpforum.com/math-he...ous-below.html

http://www.mathhelpforum.com/math-he...ng-unions.html

http://www.mathhelpforum.com/math-he...ric-space.html

http://www.mathhelpforum.com/math-he...sure-sums.html

Do you want more ?

I think it's rather scarce to see someone detailing this way, with good latex, what he's done so far, eh ?

So I guess you'd better check before saying such a thing.

Hint :

__Spoiler__: - Nov 10th 2009, 02:39 PMDrexel28
- Nov 10th 2009, 02:43 PMMoo
Not at all !

They certainly don't have the same syntax. One speaks a correct English, the other one is obviously a non native speaker !

The use of the LaTeX is not the same. And the level of the questions asked in the forums is completely different from one to another.

And I showed you 9 proofs that tttcomrader transgalactic.

Please check before saying that.

Coming from someone who's only been a member for 10 days and who apparently wasn't in this forum before that, it's quite inappropriate (Giggle) (Rofl) - Nov 11th 2009, 06:44 AMtttcomrader
lol, sorry about the lack of the work that I showed in this thread, this question is actually part of a proof that I read from the current chapter. I didn't type the whole proof out since it isn't really my original work and I only have question on that particular part.

Anyway, thank you and I appreicate the help, and again I apologize for the confusion.

So my work following the hint:

Prove that

Proof.

If , that means , implies that for some n, and that is the only one since all En are disjoint.

Then , and the arguement is the same the other way around.

If , then x is not in any of the E_n, so of course

So now, with that established, I need to think about:

Let

And

Now, can I say that to conclude the proof? - Nov 11th 2009, 07:32 AMMoo
No,

Once you've proved (well) the preliminary thing, just note that :

and of course, justify the inversion of sum and integral :) (in that case it's simple since f is positive)