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visits member for 2 years, 9 months
seen 13 hours ago

13h
comment Can conditional expectation always be realized in a standard probability space?
@ElmarZander Yes, that is right.
Sep
4
awarded  Revival
Aug
31
comment Surprise exam paradox?
Yes, but that is compatible with the model.
Aug
31
comment Is it sufficient to compare two measures on a generator?
The way you asked the question, $\mathcal{G}=\emptyset$ would be the generator.
Aug
31
answered Is it sufficient to compare two measures on a generator?
Aug
25
comment Proof that $X$ countable, $\mathcal M$ algebra on $X$ implies $\mathcal M$ a $\sigma$-algebra
@MattBrenneman 1. You cannot accept comments as answers. I reposted the comment as an answer. 2. You can only accept the answer from the account from which you asked the question "Gremlin Brenneman".
Aug
25
answered Proof that $X$ countable, $\mathcal M$ algebra on $X$ implies $\mathcal M$ a $\sigma$-algebra
Aug
25
comment Proving that multiplication of convex function is convex
@roni It is false. Take the two functions $x\mapsto x$ and $x\mapsto -x$.
Aug
24
answered Metrizability of quotient spaces of metric spaces
Aug
24
comment Proof that $X$ countable, $\mathcal M$ algebra on $X$ implies $\mathcal M$ a $\sigma$-algebra
Yes, that's right.
Aug
24
comment Proof that $X$ countable, $\mathcal M$ algebra on $X$ implies $\mathcal M$ a $\sigma$-algebra
The family of all subsets of $\mathbb{N}$ that are either finite or have a finite complement is an algebra, but not a $\sigma$-algebra.
Aug
24
revised Reinventing The Wheel - Part 2: The Lebesgue Integral
added 13 characters in body
Aug
24
revised Reinventing The Wheel - Part 2: The Lebesgue Integral
added 10 characters in body
Aug
24
answered Reinventing The Wheel - Part 2: The Lebesgue Integral
Aug
23
answered “Structure of a measure space is the coarsest among all substantial structures on a set…”
Aug
23
comment Do we need $\mu, \nu$ to be $\sigma$-finite to show $\int fg \ d(\mu \otimes \nu) = \int f \ d\mu \int g \ d\nu$?
There are various definitions of product measures out there, and some can be applied to arbitrary measure spaces. See the discussion in Fremlins treatise on measure theory in chapter 25.
Aug
23
comment When a group acts on a metric space isometrically, transitively, and faithfully, is it a closed subspace of the isometry group?
"Probably the subgroup of translations along a fixed irrational slope on the flat torus is not a closed subgroup of its isometry group." – Daniel Rust"
Aug
23
comment When a group acts on a metric space isometrically, transitively, and faithfully, is it a closed subspace of the isometry group?
Patrick Da Silva asked for his deleted comment to be reposted: @DanielRust : This is not transitive, the orbit of an element is only dense.
Aug
23
comment How many different sizes of infinity are there?
@mistermarko I don't know abut Kant, but Bell is certainly not wrong. But he never stated that it is consistent with ZF that there is "only one size of infinity". Because he has a clue about set theory.
Aug
23
comment How many different sizes of infinity are there?
@mistermarko Can you show me how it is consisten with ZF that there is an injection from the powerset of $\mathbb{N}$ into $\mathbb{N}$?