User Marios Gretsas

1 vote

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Give a sequence such that its set of accumulation points is [0,1]

answered Jan 28, 2023 at 11:51

0 votes

Borel measure taking finitely many values

answered Sep 21, 2021 at 8:23

2 votes

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Continuity of series of functions.

answered Sep 19, 2021 at 7:46

2 votes

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Is there an open bijective map from $\mathbb{R}$ to $\mathbb{R}$ that is not continuous?

answered Sep 19, 2021 at 7:14

1 vote

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Does the sequence $\displaystyle g_n(t)=\int_0^1 \frac{t f(\sqrt[n]{x})}{1+t f(\sqrt[n]{x})} dx$ converge uniformly on $[0, \infty)$?

answered Sep 18, 2021 at 13:19

1 vote

Does a non-negative integral multiplying a greater function greater than the original integral?

answered Sep 18, 2021 at 6:33

1 vote

Understanding the Proof that $\{f_n\}$ to $f$ in $L^p$ if and only if $\|f_n\|_p \to \|f\|_p$

answered Sep 17, 2021 at 20:39

1 vote

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Convergence in $\mathcal{M}$ implies convergence in measure on sets of finite measure

answered Sep 17, 2021 at 18:51

3 votes

Prove that $S=\{(x,y):|x+y|\leq 1, |xy|\leq 1\}$ is a compact set

answered Sep 17, 2021 at 15:43

1 vote

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Existence of special enumeration of the rationals

answered Sep 17, 2021 at 13:23

8 votes

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

answered Sep 17, 2021 at 10:07

1 vote

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Independence between sigma algebras

answered Sep 17, 2021 at 7:54

0 votes

Example of a non compact metric space

answered Sep 17, 2021 at 7:27

4 votes

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$A$ Lebesgue measurable iff $\forall\varepsilon>0\ \exists G=\bigcup_{n=1}^{N}I_n$ bounded open intervals: $|A\setminus G|+|G\setminus A|<\varepsilon$

answered Sep 16, 2021 at 10:35

0 votes

$X_1,X_2, \ldots$ be i.i.d. Show that $\mathbb{E}|X_1| < \infty $ iff $ \frac{X_n}{n} \to 0$ a.s

answered May 30, 2021 at 16:18

1 vote

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How do we justify that $|A+h\setminus A|\to 0$ as $|h|\to 0$?

answered Feb 27, 2021 at 16:16

2 votes

Using Egorov's Theorem when the sequence of functions converges pointwise to infinity

answered Feb 26, 2021 at 22:10

1 vote

How to prove that $\int_{[-\pi,\pi]}\log(\vert 1- \exp(it)\vert)\mathrm{d}\lambda(t)=0$?

answered Feb 24, 2021 at 1:52

1 vote

How to prove a function is a regular Borel measure on $\mathbb{R}$

answered Feb 23, 2021 at 0:48

2 votes

Quick way to see that $\sqrt{1+x^2+y^2}^{-4}$ is $L^2$-integrable

answered Feb 22, 2021 at 20:44

2 votes

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Follow up question on Folland Prop. 2.34

answered Feb 21, 2021 at 21:38

1 vote

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Fubini's theorem for Probability measure

answered Feb 21, 2021 at 21:07

1 vote

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Implication of existence of non-measurable set by Terence Tao (Analysis 2)

answered Feb 20, 2021 at 21:56

1 vote

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Prove for non-negative RV , $\mathbb{E}\{\boldsymbol{X}\}$ is finite iff $\sum_{n=0}^{\infty} \mathbb{P}(X>n \epsilon)$ converges for all $\epsilon>0$

answered Feb 19, 2021 at 23:14

1 vote

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Prove that $\forall a \in \mathbb{R} \ , \mathbb{E}\left\{|\boldsymbol{X}-\boldsymbol{a}|^{p}\right\}<\infty$ with conditions.

answered Feb 19, 2021 at 22:26

0 votes

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Beginner conditional probablity calculation

answered Feb 19, 2021 at 22:20

1 vote

Probability of time waiting for the bus

answered Feb 19, 2021 at 20:00

3 votes

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Prove that, there does not exist any $A ⊆ R$ satisfying $m(A ∩ I) = α l(I)$, for all intervals $I ⊂ R$

answered Feb 19, 2021 at 17:47

1 vote

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Convergent series proof

answered Feb 19, 2021 at 17:35

0 votes

Littlewood's First Principle with disjoint intervals

answered Sep 13, 2020 at 19:05

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875 Answers

Give a sequence such that its set of accumulation points is [0,1]

Borel measure taking finitely many values

Continuity of series of functions.

Is there an open bijective map from $\mathbb{R}$ to $\mathbb{R}$ that is not continuous?

Does the sequence $\displaystyle g_n(t)=\int_0^1 \frac{t f(\sqrt[n]{x})}{1+t f(\sqrt[n]{x})} dx$ converge uniformly on $[0, \infty)$?

Does a non-negative integral multiplying a greater function greater than the original integral?

Understanding the Proof that $\{f_n\}$ to $f$ in $L^p$ if and only if $\|f_n\|_p \to \|f\|_p$

Convergence in $\mathcal{M}$ implies convergence in measure on sets of finite measure

Prove that $S=\{(x,y):|x+y|\leq 1, |xy|\leq 1\}$ is a compact set

Existence of special enumeration of the rationals

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

Independence between sigma algebras

Example of a non compact metric space

$A$ Lebesgue measurable iff $\forall\varepsilon>0\ \exists G=\bigcup_{n=1}^{N}I_n$ bounded open intervals: $|A\setminus G|+|G\setminus A|<\varepsilon$

$X_1,X_2, \ldots$ be i.i.d. Show that $\mathbb{E}|X_1| < \infty $ iff $ \frac{X_n}{n} \to 0$ a.s

How do we justify that $|A+h\setminus A|\to 0$ as $|h|\to 0$?

Using Egorov's Theorem when the sequence of functions converges pointwise to infinity

How to prove that $\int_{[-\pi,\pi]}\log(\vert 1- \exp(it)\vert)\mathrm{d}\lambda(t)=0$?

How to prove a function is a regular Borel measure on $\mathbb{R}$

Quick way to see that $\sqrt{1+x^2+y^2}^{-4}$ is $L^2$-integrable

Follow up question on Folland Prop. 2.34

Fubini's theorem for Probability measure

Implication of existence of non-measurable set by Terence Tao (Analysis 2)

Prove for non-negative RV , $\mathbb{E}\{\boldsymbol{X}\}$ is finite iff $\sum_{n=0}^{\infty} \mathbb{P}(X>n \epsilon)$ converges for all $\epsilon>0$

Prove that $\forall a \in \mathbb{R} \ , \mathbb{E}\left\{|\boldsymbol{X}-\boldsymbol{a}|^{p}\right\}<\infty$ with conditions.

Beginner conditional probablity calculation

Probability of time waiting for the bus

Prove that, there does not exist any $A ⊆ R$ satisfying $m(A ∩ I) = α l(I)$, for all intervals $I ⊂ R$

Convergent series proof

Littlewood's First Principle with disjoint intervals