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2d
comment A simple $C_{0}$-semigroup question.
So while I have written papers on semigroup theory, I have read very little of the literature!
2d
comment A simple $C_{0}$-semigroup question.
No, I am probably wrong!
2d
comment A simple $C_{0}$-semigroup question.
I'm thinking about it even more. How do you justify the product formula? Things that work fine in finite dimensions don't necessarily follow in the infinite dimensional case.
2d
comment A simple $C_{0}$-semigroup question.
Since my proposed answer is a counterexample, I'm struggling to figure out the error in your answer. I think you need to show rigorously that $\frac d{dt} \phi(t)$ exists. (You also need to define in what space this derivative is calculated.)
2d
answered What does the conditional expectation look like when the $\sigma$-algebra is infinite
2d
answered About a matrix identity.
Aug
29
comment Does it matter if you use big $L$ or little $l$ when talking about $L$-norms?
If you make the measure space the positive integers with counting measure, then $L_p$ is the same as $\ell_p$.
Aug
28
comment Convolution of independent but 'different' probability distributions
While the interpretation you give is the only one that makes sense, I don't really see why one would make such an interpretation. Convolution is for adding real valued independent random variables. It makes no sense to add gender to age, unless you arbitrarily assign 0 to male and young, and 1 to female and old.
Aug
25
comment Expected norm of a random Gaussian vector
No, the constants won't depend upon the dimension of the vector.
Aug
24
comment Understanding the matrix normal distribution
Also the order of multiplication is only dictated by the sizes of the matrices.
Aug
24
comment Understanding the matrix normal distribution
Being "distributed according to a matrix valued normal distribution" has the property that it is closed under left or right multiplication by non-random matrices.
Aug
24
comment Expected norm of a random Gaussian vector
You can use the so called Khinchine-Kahane inequality to show that there are universal constants $c_1,c_2>0$ so that $c_1 \le E\|X\|_2 / \sqrt{E\|X\|_2^2} \le c_2$.
Aug
24
revised Understanding the matrix normal distribution
added 225 characters in body
Aug
24
answered Understanding the matrix normal distribution
Aug
24
comment Let $G$ be a compact group. If $\{a^n\}_{n \in \mathbb{Z}}$ is dense in $G$, then $G$ is abelian.
Yeah, nets can be tricky. I don't know too much about them either.
Aug
24
comment Let $G$ be a compact group. If $\{a^n\}_{n \in \mathbb{Z}}$ is dense in $G$, then $G$ is abelian.
I think it would work with nets instead of sequences. You need the additional axiom of Hausdorff to be sure that limits of nets are unique, if they exist.
Aug
24
comment Let $G$ be a compact group. If $\{a^n\}_{n \in \mathbb{Z}}$ is dense in $G$, then $G$ is abelian.
That works if the topology comes from a metric. Does it hold for general topological groups? Maybe you have to use limits of nets instead of limits of sequences.
Aug
24
answered Let $G$ be a compact group. If $\{a^n\}_{n \in \mathbb{Z}}$ is dense in $G$, then $G$ is abelian.
Aug
24
revised Limit of median of uniform distribution
Add subscript + to make sure we weren't taking powers of negative numbers.
Aug
24
comment Limit of median of uniform distribution
I cannot think of another way to do this. But Stirling's formula is quite straightforward en.wikipedia.org/wiki/Stirling%27s_approximation, and it works for the Gamma function as well as $n!$.