rgauravg
Feb8-12, 02:15 PM
Hi!
I have two question:-
(1) f:[0,1]→R, is positive and measurable function. Show that ∫_[0,1] f dμ>0,
My approch:-
I jcan think of something like ∫_[0,1] f dμ=∫fχ_[0,1]dχ which is equal to Ʃfμ([0,1])>0 is this make sence? Please give some hint, how I should approch this.
(2) Show that ∫_R f dμ=lim_n→∞∫_[-n,n] f dμ, In this I m thinking if I can use monotone convergence theorem and prove it some how. But really I dont have any nice way to explain it.
Any help or hint?
I have two question:-
(1) f:[0,1]→R, is positive and measurable function. Show that ∫_[0,1] f dμ>0,
My approch:-
I jcan think of something like ∫_[0,1] f dμ=∫fχ_[0,1]dχ which is equal to Ʃfμ([0,1])>0 is this make sence? Please give some hint, how I should approch this.
(2) Show that ∫_R f dμ=lim_n→∞∫_[-n,n] f dμ, In this I m thinking if I can use monotone convergence theorem and prove it some how. But really I dont have any nice way to explain it.
Any help or hint?