Question

Lower bound for maximal function which yields maximal function is not integrable

score 422 · Answer 1 · 2026-04-25 04:08:58

422

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Lower bound for maximal function which yields maximal function is not integrable

Published on 25 Apr 2026 - 4:08

score 237 · Answer 2 · 2026-04-11 22:15:16

237

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How to show that the closed unit ball is a measurable set for outer measure $m^*$?

Published on 11 Apr 2026 - 22:15

score 250 · Answer 3 · 2026-04-13 07:19:45

250

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Characterization Theorem of the Lebesgue Stieltjes Measure on the Real Line (Folland Theorem 1.18)

Published on 13 Apr 2026 - 7:19

score 144 · Answer 4 · 2026-04-25 04:17:14

144

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Help in understanding a property of Lebesgue measure and linear applications.

Published on 25 Apr 2026 - 4:17

score 81 · Answer 5 · 2026-04-16 06:57:25

81

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If $E\subset \mathbb R^n$ measurable then $aE$ is measurable for all $a\in\mathbb R$ and $m(aE)=a^nm(E)$

Published on 16 Apr 2026 - 6:57

score 188 · Answer 6 · 2026-04-15 23:15:39

188

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Probability that a random number belongs to $[a,b]\subseteq[0,1]$

Published on 15 Apr 2026 - 23:15

score 353 · Answer 7 · 2026-04-25 04:14:13

353

Views

Royden's Lebesgue Integration 4.4 #34

Published on 25 Apr 2026 - 4:14

score 661 · Answer 8 · 2026-04-25 04:18:10

661

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Let $E$ be a Lebesgue measurable subset of $\mathbb{R}$ such that $m(E\cap(E+t)) = 0$ for all $t \neq 0$. Then prove that $m(E)=0$.

Published on 25 Apr 2026 - 4:18

score 81 · Answer 9 · 2026-04-25 04:14:46

81

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A nice property of $L_1$ function in $[0,1]$.

Published on 25 Apr 2026 - 4:14

score 313 · Answer 10 · 2026-04-10 19:29:14

313

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Measure Theory ; why it works?

Published on 10 Apr 2026 - 19:29

score 55 · Answer 11 · 2026-04-25 05:54:56

55

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If $\{f_n\}$ is a Cauchy sequence in $(L^1,\|\cdot \|_{L^1})$ does it imply $f_n\to f$ for a certain $f\in L^1$?

Published on 25 Apr 2026 - 5:54

score 336 · Answer 12 · 2015-11-03 11:46:11

336

Views

Bounding Lebesgue measure by diameter

Published on 03 Nov 2015 - 11:46

score 2.6k · Answer 13 · 2026-04-07 07:04:16

2.6k

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Why do we consider Borel sets instead of (Lebesgue) measurable sets?

Published on 07 Apr 2026 - 7:04

score 23 · Answer 14 · 2026-04-29 14:23:40

23

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what would be $F=\bigcup_{i=1}^N [a_i,b_i]$ in $m(E\Delta F)\leq \varepsilon$ if $E=\mathbb Q$?

Published on 29 Apr 2026 - 14:23

score 63 · Answer 15 · 2026-04-14 15:37:32

63

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Functions belonging to $L_p(X,S,\lambda)$ for a single value of $p\in (0,\infty )$

Published on 14 Apr 2026 - 15:37

List Question

Lower bound for maximal function which yields maximal function is not integrable

How to show that the closed unit ball is a measurable set for outer measure $m^*$?

Characterization Theorem of the Lebesgue Stieltjes Measure on the Real Line (Folland Theorem 1.18)

Help in understanding a property of Lebesgue measure and linear applications.

If $E\subset \mathbb R^n$ measurable then $aE$ is measurable for all $a\in\mathbb R$ and $m(aE)=a^nm(E)$

Probability that a random number belongs to $[a,b]\subseteq[0,1]$

Royden's Lebesgue Integration 4.4 #34

Let $E$ be a Lebesgue measurable subset of $\mathbb{R}$ such that $m(E\cap(E+t)) = 0$ for all $t \neq 0$. Then prove that $m(E)=0$.

A nice property of $L_1$ function in $[0,1]$.

Measure Theory ; why it works?

If $\{f_n\}$ is a Cauchy sequence in $(L^1,\|\cdot \|_{L^1})$ does it imply $f_n\to f$ for a certain $f\in L^1$?

Bounding Lebesgue measure by diameter

Why do we consider Borel sets instead of (Lebesgue) measurable sets?

what would be $F=\bigcup_{i=1}^N [a_i,b_i]$ in $m(E\Delta F)\leq \varepsilon$ if $E=\mathbb Q$?

Functions belonging to $L_p(X,S,\lambda)$ for a single value of $p\in (0,\infty )$

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