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9h
awarded  Notable Question
1d
comment Necessary to assume $f\in C^\infty$ in this Fourier transform problem?
@CameronWilliams Yes, indeed. I'm inclined to just say the problem is not very tightly constructed, but given the rate at which I make errors, I thought it was wise to check...
1d
revised Necessary to assume $f\in C^\infty$ in this Fourier transform problem?
edited body
1d
asked Necessary to assume $f\in C^\infty$ in this Fourier transform problem?
1d
accepted A $\mathbb Z/p\mathbb Z[G]$ submodule with no complement
1d
comment A $\mathbb Z/p\mathbb Z[G]$ submodule with no complement
Interesting. Thank you.
1d
comment A $\mathbb Z/p\mathbb Z[G]$ submodule with no complement
I think this is false when $|X|=4$...
1d
asked A $\mathbb Z/p\mathbb Z[G]$ submodule with no complement
Jul
28
answered Continuity of the roots of a polynomial in terms of its coefficients
Jul
28
comment Is there accepted notation for the pushforward measure that doesn't mention $\mathbf{P}$?
@goblin That was mostly in jest. But really, you realize that (as far as I know) no definition of "measurable function" in common use requires that function to have the probability measure of its domain as a datum? The definition you have in mind seems to be your invention. Which is fine, I suppose, but it would probably be worth noting in questions like these that you're doing slightly nonstandard mathematics. Otherwise, it looks like you're just confused!
Jul
28
comment Is there accepted notation for the pushforward measure that doesn't mention $\mathbf{P}$?
@NateEldredge Sure. What I'm objecting to is what looks to me like a philosophical confusion brought about by a poor choice of notation.
Jul
28
comment Is there accepted notation for the pushforward measure that doesn't mention $\mathbf{P}$?
@goblin With all due respect, you are not Bourbaki.
Jul
28
comment Is there accepted notation for the pushforward measure that doesn't mention $\mathbf{P}$?
A function is a set of ordered pairs satisfying a certain condition. If I just hand you $X$ as a set of ordered pairs and tell you that it's a measurable function between two measure spaces, you cannot in general recover either measure uniquely.
Jul
28
comment Is there accepted notation for the pushforward measure that doesn't mention $\mathbf{P}$?
But the question you're asking seems to arise exactly from the kind of confusion that comes from conflating them. It's simply not true that $X$, defined as a function, contains any information about the measure on its domain.
Jul
28
comment Is there accepted notation for the pushforward measure that doesn't mention $\mathbf{P}$?
Also, usually $\mathcal M$ is reserved for the collection of measurable sets on space, not the space itself.
Jul
28
comment Is there accepted notation for the pushforward measure that doesn't mention $\mathbf{P}$?
It's been a while since I've thought about these things, but I think there's some confusion with the way you've set things up. The probability space and the measure on that space are different objects, but you seem to conflate them. You don't push forward the space, you push forward the measure on that space. And $X$ may "know" its domain, but it doesn't "know" the measure on that domain.
Jul
24
comment Riemann mapping under which uncountably many boundary points correspond to a single point
Wonderful. $\bf{}$
Jul
24
accepted Riemann mapping under which uncountably many boundary points correspond to a single point
Jul
23
awarded  Revival
Jul
22
accepted When does a Galois group of a quintic have order divisible by three?