1-)if is measurable then show that

2-)if f(x) is nonnegatif and integrable function than show that

m{ }=0

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- Dec 17th 2008, 09:02 AMsah_matreel analysis-help(added some more questions)
1-)if is measurable then show that

2-)if f(x) is nonnegatif and integrable function than show that

m{ }=0 - Dec 18th 2008, 03:12 AMMoo
Hello,

Remember that a measure is -additive : if , then

**1.**

Proof :

It is obvious that and note that

So from -additivity, we've proved that.

**2.**

Proof :

, and are disjoint 2 by 2.

And their union is

So by -additivity,

Add to each side of the equality :

By**1.**:

and

You're done. - Dec 18th 2008, 06:23 AMsah_mat
thans a lot mr.moo,what do u think about the second question,i think it is a lemma but ı could not find it.i hope some of my friends here help my questions,becouse these are may be my exam questions at next week,and my last chance to pass reel analysis.

i appreciate your helps. - Dec 21st 2008, 03:39 AMsah_matsome more questions ı want to ask
question1)

if f(x) is nonnegative and integrable funciton at then prove is continuous.

question2)

if f(x) is integrable funciton at [a,b] then prove the function is continuous at [a,b]

question3)

if the set of reel number { } n=1 to is disjoint two by two,then construct such sets { } n=1 to

which holds

i have already been thankfull for helps ı am trying to solve other questions .i wish the citizens of math help forum are going to help me.(Bow) - Dec 24th 2008, 02:50 PMsah_mat
ı have 6 hours to my make up exam but i can not solve this questions,if there is someone hearing my plea come on anad help meeeeee!!!i am still studying i will check with all my hope after 4 hours.thanks a lot.