2,505 reputation
731
bio website math.uni-trier.de/~wengenroth
location Universität Trier
age 47
visits member for 2 years, 11 months
seen 43 mins ago
I am Professor for Mathematics at the Unversität Trier (Germany)

Jan
23
comment Generating random variables from the Cantor Distribution
If you agree that you can create a Bernoulli sequence from the Cantor distribution then $U=\sum_{j=1}^\infty 2^{-j}B_j$ is uniformly distributed.
Jan
23
comment Characterizations of an exotic measure on the open sets in the circle $S^{1}$
Sorry, but I do not understand the definition of $\mu_n$. There is no $U$ on the right hand side.
Jan
23
comment Generating random variables from the Cantor Distribution
Wasn't the question the other way round? However, from a Cantor distribution you can get a Bernoulli sequence which gives you a uniform distribution and hence every distribution on $\mathbb R$.
Jan
22
comment Discrete measures and discrete kernels
To have measurability with respect to $x$ you should assume measurability of the functions $y_l$. Then $K$ should be indeed a kernel.
Jan
11
comment Getting a measure from a premeasure through an adjoint
What about the measurable and measure preserving maps as morphisms? The Caratheodory construction does not really give back the the measure space $(X,\mathscr F,\mu)$ but its completion.
Jan
11
comment symbol $m\in L^{\infty}$ implies any boundedness of a bilinear operator?
Isn't $T$ the multiplier operator on $L^2(\mathbb R^2)= L^2(\mathbb R) \hat \otimes L^2(\mathbb R)$? Note that the Fourier tranform of $f\otimes g$ is $\hat f(\xi) \hat g(\eta)$.
Jan
11
awarded  Custodian
Jan
11
reviewed Approve Commutator with a generator of a free group
Jan
5
answered Example of noncomplete quotient of complete lcs mod closed subspace
Dec
17
comment Is there a simple direct proof of the Open Mapping Theorem from the Uniform Boundedness Theorem?
Well, well,... I consider "the rest of the proof" as the main point of the OMT. In Rudin's book, this is even part of the statement.
Dec
8
comment Can one show that the dual of a quasi-Banach space separates points without explicitly identifying the dual?
A trivial sufficient condition is that $X$ embeds continuously into some Hausdorff locally convex space $Y$.
Dec
8
comment Is every sigma-algebra the Borel algebra of a topology?
@Freeze_S No, it is the first uncountable ordinal.
Dec
1
comment Defining density of a random function using Radon-Nikodym Theorem
To stimulate this thread you should try to say more precisely what you are looking for. As stated, your question does not make much sense (you could take $\mu=P_X$ and density $1$). For $E=C([0,\infty))$ the Wiener measure (distribution of Brownian motion) is certainly an interesting measure on $E$, but without more context it is not clear whether this is an interesting case for you.
Dec
1
comment Bounded operator on a normed space with empty spectrum
The general fact Alexander is referring to is sometimes called "abstract Mittag-Leffler theorem" (a version of this is e.g. in Bourbaki). The first explicit appearance however is in an article of R. Arens from 1958.
Dec
1
comment Extend product sigma-algebra to cross-constant sets
Isn't it just the axiom of choice which excludes a "Lebesgue measure " on the power set of $[0,1]$?
Nov
28
comment Defining density of a random function using Radon-Nikodym Theorem
Do you mean that $E$ is a Banach space of real-valued functions on $[0,1]$ (like $E=C([0,1])$) and $X:\Omega \to E$ is a process with paths in $E$? Anyway, if you do not have a reference measure on $E$ it makes no sense to speak about "the density".
Nov
25
comment decomposition of tempered distributions by entire analytic functions
I guess you mean by $g^\vee$ the inverse Fourier transform. Since Fourier transformation is an isomorphism $\mathscr S'\to\mathscr S'$ (with the weak*-topology) you need to show that $\sum\limits_{k=1}^K \phi_k \hat f$ converges to $\hat f$ and hence $\langle \sum\limits_{k=1}^K \phi_k \hat f,g \rangle \to \langle \hat f ,g\rangle$ for all $g\in\mathscr S$ (where$\langle f,g \rangle$ denotes the duality between $\mathscr S'$ and $\mathscr S$). For this it would be enough to show $\sum\limits_{k=1}^K \phi_kg \to g$ in $\mathscr S$ and this will depend on bounds for the derivatives of $\phi$.
Nov
25
comment Continuity of a Functional
The question is not clear. What is the domain of $T$? Do you mean by $F^{-1}(s)$ the multiplicative inverse $1/F(s)$?
Nov
24
awarded  Nice Answer
Nov
20
comment Between compact and locally uniform: What is the name of this convergence?
Very informative answer. A reference would be nice.