1-)if is measurable then show that
2-)if f(x) is nonnegatif and integrable function than show that
m{ }=0
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.
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.
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.