# Tagged Questions

Convergence of sequences and different modes of convergence.

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### Coconvergent topology basis?

Consider the space $X=\{\frac1n:n\in\mathbb N_+\}$, with the "coconvergent topology": $$\mathcal O=\{A:(A=\varnothing)\lor(\sum_{x\notin A}x<\infty)\}$$ That is, a nonempty set is open iff its ...
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### Limit of $\frac{1}{2^n}\sum_{n=0}^{2^n-1}f(e^\frac{2k\pi}{2^n}i)$ for a complex-analytic function

Let consider a Laurent series $\displaystyle{ \sum_{k\in\mathbb Z}a_kz^k }$ with complex coefficients and converging inside the annulus $A=\{\ z\in\mathbb C\ |\ r<|z|<R\ \}$, with $r<1<R$....
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Let $X$ be a compact metric space, $\mu$ a Borel measure and $f_{n} \in L^{1}(X,\mu)$ continuous functions such that $f_{n}(x) \overset {L^{1}} \rightarrow 0$. Now can we deduce that $\frac{1}{n}\... 0answers 37 views ### Convergence of sum of antiderivative and derivative This question is inspired by this question: Solutions for$ \frac{dy}{dx}=y $?. It makes me wonder if there are any function where the sum of all antiderivative and derivative converges. The question:... 0answers 47 views ### Asymptotic Bounds for the distribution of$f_n(X_n)$. Let$\{X_n\}_{n \in \mathbb{N}}$be a sequence of$\mathbb{R}^{k}$-valued random variables defined on some probability space$(\Omega, \mathcal{F}, \mathbb{P})$converging almost surely to$X$. ... 0answers 78 views ### snails on a tetrahedron suppose you have$4$snails arranged on the surface of an equilateral tetrahedron(all sides equal, each snail is numbered from$1$to$4$, and that the snail numbered$1$moves toward snail numbered$...
Let $\Omega \subset \mathbb{R}^{n}$ be bounded and open. Assume that $a: \Omega \times \mathbb{R} \times \mathbb{R}^{n} \rightarrow \mathbb{R}^{n}$ is a Caratheodory function which means $a(x,.,.)$ is ...