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2 votes

Completion of metric space (Terence Tao Analysis II Exercise 1.4.8 part (c))

answered May 20, 2021 at 22:56

1 vote

Prove that $\sqrt{2}$ is irrational using strong induction

answered May 24, 2021 at 21:17

1 vote

Accepted

Derivation of equations using a general waterpipe problem

answered May 27, 2021 at 2:47

1 vote

$(X,d)$ Complete and totally bounded $\iff $ $(X,d)$ is compact

answered May 31, 2021 at 7:27

1 vote

The Typewriter Sequence

answered Mar 5, 2023 at 2:03

1 vote

Show that $1 /(1-x)$ is real analytic

answered Oct 21, 2021 at 23:27

1 vote

the proof of several variable calculus chain rule

answered Dec 17, 2021 at 5:35

1 vote

open box $(0, 1/q)^n$ and closed box $[0, 1/q]^n$ both have measure $1/q^n$.

answered Jan 2, 2022 at 22:08

1 vote

Lebesgue integral of $f$ is equal to the Lebesgue measure of the area under the curve of $f$

answered Apr 20, 2022 at 3:38

1 vote

Accepted

Proving the Lebesgue measure space completes the Borel measure space

answered Feb 9, 2023 at 18:39

1 vote

Linear Change of Variables for Measurable Functions

answered Apr 23, 2022 at 7:25

1 vote

Construction of a Borel set with positive but not full measure in each interval

answered Jun 1, 2023 at 21:15

1 vote

Fast $L^{1}$ Convergence implies almost uniform convergence

answered Mar 8, 2023 at 22:15

1 vote

Measurable group homomorphisms are continuous

answered Mar 27, 2023 at 21:30

1 vote

A cube of density

answered Apr 21, 2023 at 22:59

1 vote

Yet another definition of uniform integrability. Is it equivalent to the classical definition by G.A. Hunt?

answered Mar 18, 2023 at 19:28

1 vote

Accepted

One-sided Hardy-Littlewood inequality for monotone function

answered Jun 26, 2023 at 21:58

1 vote

Horizontal\Vertical truncation lemmas

answered Aug 12, 2023 at 14:44

1 vote

Accepted

Second Borel-Cantelli lemma via the moment method

answered Feb 15 at 21:04

1 vote

Number of triangles in Erdös-Renyi graph

answered Feb 21 at 21:05

1 vote

Convergence/divergence of the operator norm for random sign matrices

answered Mar 6 at 8:34

1 vote

A convergence property for iid sequence of Cauchy random variables

answered Jun 21 at 0:43

1 vote

Lack of strong law for triangular array

answered Jul 12 at 16:19

0 votes

Concentration around the mean in Cramer random model

answered Apr 25 at 5:46

0 votes

Uniform bound involving trace of random matrix

answered Apr 23 at 20:25

0 votes

Probabilistic Riemann hypothesis under Cramér random model

answered May 4 at 3:23

0 votes

Probabilistic Goldbach conjecture under Cramér random model

answered May 9 at 23:27

0 votes

Is the limit of uniformly integrable functions integrable?

answered Mar 19, 2023 at 23:03

0 votes

Rising Sun Inequality (Dunford-Schwartz maximal inequality)

answered Apr 2, 2023 at 23:57

0 votes

Every dominated sequence of measurable functions is uniformly integrable?

answered Mar 17, 2023 at 23:37

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42 Answers

Completion of metric space (Terence Tao Analysis II Exercise 1.4.8 part (c))

Prove that $\sqrt{2}$ is irrational using strong induction

Derivation of equations using a general waterpipe problem

$(X,d)$ Complete and totally bounded $\iff $ $(X,d)$ is compact

The Typewriter Sequence

Show that $1 /(1-x)$ is real analytic

the proof of several variable calculus chain rule

open box $(0, 1/q)^n$ and closed box $[0, 1/q]^n$ both have measure $1/q^n$.

Lebesgue integral of $f$ is equal to the Lebesgue measure of the area under the curve of $f$

Proving the Lebesgue measure space completes the Borel measure space

Linear Change of Variables for Measurable Functions

Construction of a Borel set with positive but not full measure in each interval

Fast $L^{1}$ Convergence implies almost uniform convergence

Measurable group homomorphisms are continuous

A cube of density

Yet another definition of uniform integrability. Is it equivalent to the classical definition by G.A. Hunt?

One-sided Hardy-Littlewood inequality for monotone function

Horizontal\Vertical truncation lemmas

Second Borel-Cantelli lemma via the moment method

Number of triangles in Erdös-Renyi graph

Convergence/divergence of the operator norm for random sign matrices

A convergence property for iid sequence of Cauchy random variables

Lack of strong law for triangular array

Concentration around the mean in Cramer random model

Uniform bound involving trace of random matrix

Probabilistic Riemann hypothesis under Cramér random model

Probabilistic Goldbach conjecture under Cramér random model

Is the limit of uniformly integrable functions integrable?

Rising Sun Inequality (Dunford-Schwartz maximal inequality)

Every dominated sequence of measurable functions is uniformly integrable?