bio  website  thatsmathematics.com 

location  Colorado  
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visits  member for  5 years, 5 months 
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2h

awarded  Necromancer 
Aug
26 
revised 
Meager subgroups of compact groups
fix typo in title 
Aug
25 
revised 
Error for the convergence by distribution
tag 
Aug
24 
comment 
Restriction of a semigroup to a form domain
I should have said, of course, that this is the case where $H = L^2(X, \mu)$ for an arbitrary measure space $(X,\mu)$. 
Aug
24 
comment 
Restriction of a semigroup to a form domain
Thanks to the spectral theorem, it should suffice to consider the case where $A$ is multiplication by a measurable function $h$ which is bounded below. In that case $T(t)$ is multiplication by $e^{th}$. It seems like the question may be easy to answer in that case. Slogan: "The spectral theorem: reducing functional analysis to measure theory since 1929." 
Aug
19 
comment 
Convergence of approximate quadratic variation in $L^p$
What if the quadratic variation is not in $L^p$ at all? 
Aug
18 
comment 
Does there exist an uncountable partition of a Polish space so that the union of any collection of blocks is Borel?
@William: If the partition has size $2^{\aleph_0}$ then by choosing subsets of the partition we get $2^{2^{\aleph_0}}$ distinct Borel sets, which is impossible. 
Aug
18 
comment 
Does there exist an uncountable partition of a Polish space so that the union of any collection of blocks is Borel?
It took me a moment to understand $f$. Another way to describe it: Using AC, choose one element $x_i$ from each $P_i$, and set $f(x) = x_i$ if $x \in P_i$. For any Borel set $B$, we have $f^{1}(B) = \bigcup_{i : x_i \in B} P_i$ which by assumption is Borel. So $f$ is Borel. 
Aug
18 
comment 
Does there exist an uncountable partition of a Polish space so that the union of any collection of blocks is Borel?
Trivial observation: all but countably many $A \in P$ must be uncountable (and hence have $A = \mathfrak{c}$). For suppose there is an uncountable $P_c \subset P$ with every $A \in P_c$ countable. Since we are assuming $\lnot \mathsf{CH}$, we can find $P_0 \subset P_c$ with $\aleph_0 < P_0 < \mathfrak{c}$. Then $B = \bigcup P_0$ has cardinality $P_0$, which cannot be if $B$ is Borel. 
Aug
18 
comment 
The union of weighted compact supported continuous function
Your last sentence asks about the $\subset$ direction of the equality, but the $\supset$ direction need not hold. Consider something like $\Omega = \mathbb{R}$, $v = 1+1_{(0, +\infty)}$. You can take $v_n$ to be 1 on $(\infty, 0]$, 2 on $[1/n, +\infty)$, and linear in between. If you take $f \in C_c(\mathbb{R})$ which is 1 in a neighborhood of 0, then $f \in C_c(\Omega, v_n)$ for every $n$, but $f \notin C_c(\Omega, v)$. 
Aug
17 
awarded  Nice Answer 
Aug
16 
revised 
Does there exist a norm on continuous realvalued function space?
added 17 characters in body 
Aug
16 
answered  Does there exist a norm on continuous realvalued function space? 
Aug
16 
comment 
Looking for the name of a mathematical symbol that looks remotely like 1 (answer: indicator function)
I removed the specialfunctions tag; that is meant for things like Bessel functions. 
Aug
16 
revised 
Looking for the name of a mathematical symbol that looks remotely like 1 (answer: indicator function)
edited tags 
Aug
16 
comment 
Looking for the name of a mathematical symbol that looks remotely like 1 (answer: indicator function)
The symbol is simply "blackboard bold 1". 
Aug
16 
comment 
Looking for the name of a mathematical symbol that looks remotely like 1 (answer: indicator function)
See tex.stackexchange.com/questions/488/blackboardboldcharacters 
Aug
16 
comment 
Looking for the name of a mathematical symbol that looks remotely like 1 (answer: indicator function)
tex.stackexchange.com is where this question belongs. 
Aug
11 
comment 
“Universal” connected spaces
Is $\kappa + 1$ here meant to be the least cardinal larger than $\kappa$, or what? 
Aug
8 
revised 
Is there a name for a partial order in which there is a countable chain which “dominates” the whole space?
added 234 characters in body 