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Dec
6
awarded  Cleanup
Nov
5
comment Clarification on increasing sequence of functions
As there has been discussion about different notions of “increasingness” I just want to point out that this is the measure theoretic definition that OP wants. It’s very important for the Beppo Levi Theorem and standard procedure proofs (approximation of functions by increasing simple functions) in measure theory.
Nov
3
revised If $\mathrm{E} |X|^2$ exists, then $\mathrm{E} X$ also exists
switched q and p in subset equation
Nov
3
comment If $\mathrm{E} |X|^2$ exists, then $\mathrm{E} X$ also exists
The inequalities that I know would already assume the finite mean (or in other words integrability) of $X$. But maybe there are other versions that only assume quasi-integrability. The explanations of @Michael Hardy and drhab seem to be the simplest for this ($p=1,q=2$) case.
Nov
3
answered If $\mathrm{E} |X|^2$ exists, then $\mathrm{E} X$ also exists
Oct
26
accepted Proof of the progressiveness of a stopped progressive process
Oct
26
comment Proof of the progressiveness of a stopped progressive process
Thank you for your comment. I didn’t know it suffices to check the measurability on the generator set. I used a similar construction as yours for arbitrary sets which involved an uncountable union, which was very hard to approximate. The “generator lemma” is very nice and was straight-forward to prove.
Oct
26
asked Proof of the progressiveness of a stopped progressive process
Jun
1
awarded  Enthusiast
Jul
6
awarded  Editor
Jul
6
awarded  Teacher
Jul
6
revised Is Dirichlet function Riemann integrable?
correction
Jul
6
comment Is Dirichlet function Riemann integrable?
Yes, that's what I meant, I will correct it.
Jul
6
answered Is Dirichlet function Riemann integrable?
Jun
27
awarded  Scholar
Jun
27
accepted A case of the central limit theorem
Jun
21
awarded  Organizer
Jun
21
revised Help understanding the difference between the LLNs and CLT?
added tag probability theory
Jun
21
suggested approved edit on Help understanding the difference between the LLNs and CLT?
Jun
21
awarded  Supporter