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Sep
25
comment $C_c(X)$ dense in $L_1(X)$
Do you not need to show that $h\bar{s_n}$ has compact support?
Sep
25
accepted $C_c(X)$ dense in $L_1(X)$
Sep
25
comment $C_c(X)$ dense in $L_1(X)$
Yay!! I get it! Finally!! Thank you!
Sep
25
comment $C_c(X)$ dense in $L_1(X)$
Oh. That follows from $s_n$ being in $L^1$, right?
Sep
25
comment $C_c(X)$ dense in $L_1(X)$
What I still don't understand is: if I want to assume I have simple functions $s_n$ that converge to $f$ pointwise, without spelling them out, how do I get $\tilde{s_n}$ with finite support?
Sep
25
comment $C_c(X)$ dense in $L_1(X)$
OK, maybe not : ( The sets in the support of $s_n$ are not compact : (
Sep
25
comment $C_c(X)$ dense in $L_1(X)$
But if "finite support" is used to mean "support of finite measure" question a) becomes trivial: a simple function already has support of finite measure in $\Omega$.
Sep
25
comment Smooth functions with compact support are dense in $L^1$
Thanks for pointing it out, that was a typo, I corrected it!
Sep
25
revised Smooth functions with compact support are dense in $L^1$
added 2 characters in body
Sep
25
accepted Homology relative to a point
Sep
25
asked Smooth functions with compact support are dense in $L^1$
Sep
25
comment $C_c(X)$ dense in $L_1(X)$
What does "I should something to you" mean?
Sep
25
comment $C_c(X)$ dense in $L_1(X)$
Thank you! About the measurable function with compact support: the step function $s_n$ has finite support and therefore compact support. This is what I meant.
Sep
24
revised $C_c(X)$ dense in $L_1(X)$
added 15 characters in body
Sep
24
comment $C_c(X)$ dense in $L_1(X)$
Did you use the Tietze theorem anywhere?
Sep
24
comment $C_c(X)$ dense in $L_1(X)$
Thanks! Where do you get the increasing sequence from? $\sigma$-finite doesn't give you that: en.wikipedia.org/wiki/%CE%A3-finite_measure
Sep
23
accepted Homology groups of unit square with parts removed — revisited
Sep
23
accepted Why is an integral domain a commutative ring with unity?
Sep
23
asked $C_c(X)$ dense in $L_1(X)$
Sep
23
accepted Lie algebra of $GL_n(\mathbb{C})$