Question

If I have a sequence of \(\mathcal{M}\)-measurable sets where \(E_1\subset E_2 \subset E_3.....\), and \(E=\cup_{n=1}^\infty E_n\) how can I show that \(\chi_{E_n} f\rightarrow\chi_Ef\) pointwise.

Answer 1

CALCULAS?

Answer 2

Measure Theory.

Answer 3

/real analysis

Answer 4

your beyond me

Answer 5

This might be one for stack math, I haven't seen many questions at this level here.

Answer 6

there are a few people here that help me. I am in no rush. Just need to wait for @eliassaab :)

Answer 7

@zzr0ck3r Is forever alone.

Answer 8

:)

Answer 9

I think I just figured it out:)

if x is in the intersection it is in E_n for some n, since the the sequence of sets is increasing, we have that its in all E_k for k>n

if x is not in E then x is not in E_n for all n,

either way we have convergence.

Answer 10

You mean
if x is in the union

Answer 11

correct:)

Answer 12

im really starting to get this stuff:)