9,721 reputation
23677
bio website thatsmathematics.com
location Colorado
age
visits member for 5 years, 5 months
seen yesterday

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 real-valued function space?
added 17 characters in body
Aug
16
answered Does there exist a norm on continuous real-valued function space?
Aug
16
comment Looking for the name of a mathematical symbol that looks remotely like 1 (answer: indicator function)
I removed the special-functions 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/blackboard-bold-characters
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