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shalop
  • Member for 7 years, 5 months
  • Last seen more than a month ago
  • NYC
22 votes
Accepted

Is there a slowest divergent function?

20 votes
Accepted

Inverse of a function's integral

19 votes
Accepted

Maximizing the value of $\int_0^1 f(x)f^{-1}(x)\ \mathrm dx$

17 votes
Accepted

(Elementary) Markov property of the Brownian motion

17 votes
Accepted

A complete subset of a metric space is closed?

14 votes
Accepted

A function whose antiderivative equals its inverse.

13 votes
Accepted

Fractional Brownian Motion and Fractional Laplacian

13 votes

Is there an example of a non compact operator whose square is compact?

12 votes
Accepted

If $f(A)\to A^{-1}$, prove that $f$ is continuous.

11 votes
Accepted

Why does the characteristic function always exist?

10 votes

If $f(x+1)+f(x-1)=\sqrt 3 f(x), \forall x$ then $f$ is periodic.

9 votes
Accepted

Why a infinite dimensional vector space over $\mathbb F_2$ is uncountable?

9 votes
Accepted

Show that $\frac1n\max\limits_{1\le i \le n } X_i\to0$ almost surely, with no independence assumption

8 votes

Law of large numbers for non-identically distributed Bernoulli random variables

8 votes

Graph of real continuous function has measure zero

8 votes
Accepted

$\lim_{n\to ∞} \left[\frac{f\left( x +\frac1n\right)}{ f(x)}\right]^n$

8 votes

Does $|f'(x)|<1$ imply $f$ has a fixed point?

7 votes
Accepted

Distribution of the Maximum of a (infinite) Random Walk

7 votes

Density of $C^\infty(\mathbb{R}^n)$ in $C^0(\mathbb{R}^n)$

7 votes

Comparing different topologies on the Hilbert cube $H = \prod_{n \in \mathbb{N}} [0,\frac 1n]$

7 votes

how to evaluate the product $\prod _{n=2}^\infty (1+ \frac{1}{n^2}+\frac{1}{n^4}+\frac{1}{n^6}+\cdots )$?

7 votes
Accepted

Operator $T \colon L^p \to L^p$ is a conditional expectation

7 votes

In a Hausdorff space the intersection of a chain of compact connected subspaces is compact and connected

7 votes
Accepted

Let $(X,\mathcal M, \mu)$ be a measure space, and $\mu_0$ the semifinite part of $\mu$. Show that there is a measure $\nu$ such that $\mu=\mu_0+\nu$.

6 votes
Accepted

Borel $\sigma$-algebra of continuous functions

6 votes
Accepted

Generating the Borel $\sigma$-algebra on $C([0,1])$

6 votes
Accepted

Show that a countable dense subset $D \subset X$ is not a $G_{\delta}$

6 votes

How to show that if $\prod X_\alpha$ is Hausdorff or normal then so is $X_\alpha $?

6 votes

$\{a_n\}$ is a sequence of nonnegative real numbers satisfying $a_{n+1} \leq a_n + \frac{(-1)^n}{n}$. Prove convergence.

6 votes
Accepted

Sample path of Brownian motion Hölder continuous?

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