Marios Gretsas

Κάτω Νευροκόπι, Δράμα, Ελλάδα

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Convergence of a series of translations of a Lebesgue integrable function

real-analysis measure-theory convergence lebesgue-integral lebesgue-measure asked Aug 23, 2017 at 1:41

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9 votes

Infinite limit of a differentiable function

calculus real-analysis limits derivatives proof-verification asked Jan 1, 2018 at 16:47

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8 votes

Ergodicity of a skew product

measure-theory fourier-analysis dynamical-systems fourier-series ergodic-theory asked Jan 20, 2018 at 0:27

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7 votes

How does ring theory connects with analysis?

soft-question asked Mar 29, 2017 at 23:13

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6 votes

Proving that a continuous $\frac{1}{\sqrt{n}}-$periodic function is constant

real-analysis proof-verification continuity asked Jul 23, 2017 at 19:06

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6 votes

High school contest math problem

real-analysis calculus limits contest-math solution-verification asked Dec 31, 2019 at 13:27

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5 votes

Example of a space that is not a topological manifold.

real-analysis general-topology differential-geometry manifolds asked Sep 14, 2018 at 11:53

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5 votes

Limit almost everywhere of averages of uniformly bounded and integrable functions .

real-analysis measure-theory lebesgue-measure asked Nov 29, 2018 at 11:34

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5 votes

The final segment topology of the naturals

general-topology asked Sep 1, 2016 at 16:50

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5 votes

The Heine-Borel theorem

real-analysis general-topology metric-spaces asked Sep 11, 2016 at 18:31

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Top Answers

Find the limit of the following Sequence

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Examples of closed sets with empty interior

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Prove convergence of the sequence $(z_1+z_2+\cdots + z_n)/n$ of Cesaro means

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How to prove the sequence $\sqrt[n!]{n!}$ has a limit

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If $\ \sum_{k=1}^n m(E_k) > n-1,$ then prove that $\bigcap_{k=1}^n E_k$ has positive measure.

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Does $\sum_{n=1}^\infty a_n^2 \text{ converges },\ a_n \geq 0 \implies \sum_{n=1}^\infty \frac{a_n}{n} \text{ converges}$?

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Compute a limit without L'Hopital's rule $\lim_{x \to a} \frac{a^x-x^a}{x-a}$

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Interesting Proofs about Metric Spaces?

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Finding the limit of $ \lim_{x\to0} \frac {\sqrt[3]{1+x} - 1} {x} $

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Pre-image of Hausdorff space is Hausdorff

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Calculate inner product of two vectors

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Find an element $\theta \in \mathbb{R}$ such that $\mathbb{Q}(\sqrt{2},\sqrt[3]{5}) = \mathbb{Q}(\theta)$

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Suppose that $\lim\limits_{n\to\infty} a_n = 1$. Is it necessarily true that $\lim\limits_{n\to\infty} (a_n)^n=1$?

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Distance from a point in a set to a subset of that set is Lipschitz

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What is the limit of the sequence $(a_n : n \in \mathbb N)$ defined by $a_n = \frac{1}{n}\sqrt[n]{1^2 + 2^2 + ... + n^2}$?

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Riemann Integrability and Jordan Measure

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If $x, y \in X$ with $x \neq y$, then there exists $f \in X^*$ such that $f(x) \neq f(y)$.

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Find $\lim_{x \to \infty} \left({\frac{x^k}{1+x+...+x^k}}\right)^{1+2x}$

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Compute the limit of $\displaystyle\lim_{n \to \infty} \int_0^1 \frac{e^{-nt}}{\sqrt{t}} \, dt$

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Finding the limit as $x$ approaches $0$

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Let $f\in L^1(R)$ set $f_n(x)=\dfrac{f(nx)}{n}$ prove that $\lim_{n \to \infty}f_n=0$ for a.e x

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How can we prove that in $\mathbb{R}^n$ if $A$ and $B$ are both closed subsets, then $A+B$ is an $F_\sigma$ set?

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Does $\sum\frac{\cos(n+1)\pi}{(2n)!}$ converge or diverge

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Limit $\lim_{n \to \infty}\sqrt[n]{1^{10}+2^{10}+\dots+n^{10}}$

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If $\sum_{n=0}^\infty a_n$ converges and $a_n>0$, does $\sum_{n=0}^\infty \sqrt{a_na_{n+1}}$ converge?

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$\lim_{(x,y)\rightarrow (0,0)}\frac{x^5-\sin(y^3)}{4x^4+3y^2}$

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Is $f^2$ is uniformly continuous

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Is this a valid proof for $\sqrt5$ being irrational?

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Find the limit of the sequence $a_n=n\sin{\frac{\pi}{2n}}$

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How to prove n! is equivalent to $n^n$?

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