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2d
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".
2d
answered Proof that $X$ countable, $\mathcal M$ algebra on $X$ implies $\mathcal M$ a $\sigma$-algebra
2d
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 $\mathbb{N}$?
Aug
23
comment Locally convex topological vector space using semi norms
1. You only have to show that it contains an open and convex set. That you can take them to be balanced and absorbing is something that you can the derive. 2. Even if you want to prove all three properties, you can simply ask yourself how one derives the topology from the family of seminorms and use that.
Aug
23
comment In how many ways can 5 distinct objects can be distributed.
Maybe you could try to edit your question and anser a bit. I understand that you are excited now, but this is a question&answer site and remarks like "OK! I got it." are not really timeless.
Aug
23
comment Why is “the set of all sets” a paradox?
@GeorgeChen There is something in set theory called a transitive set, and for such a set, every element is a subset. Here is an example: $\{\emptyset\}$.
Aug
22
comment How many different sizes of infinity are there?
I understand what Bell writes, but I don't understand what this has to do with the question.
Aug
19
awarded  Necromancer