Question

Is $\overline{D}_{\varepsilon}$ a connected Jordan region in $\mathbb{R}^{n}?$

score 198 · Answer 1 · 2026-04-12 00:52:23

198

Views

Is $\overline{D}_{\varepsilon}$ a connected Jordan region in $\mathbb{R}^{n}?$

Published on 12 Apr 2026 - 0:52

score 70 · Answer 2 · 2026-04-14 05:45:47

70

Views

Sets cut into two halves of equal size by any straight line through a particular point

Published on 14 Apr 2026 - 5:45

score 1.5k · Answer 3 · 2026-04-14 16:06:16

1.5k

Views

Can we find uncountably many disjoint dense measurable uncountable subsets of $[0,1]$?

Published on 14 Apr 2026 - 16:06

score 874 · Answer 4 · 2026-04-14 07:58:02

874

Views

Is the intersection of the following closed and open set closed? Generally?

Published on 14 Apr 2026 - 7:58

score 46 · Answer 5 · 2026-04-09 18:29:52

Is there an easy proof that the set of $x \in [0,1]$ whose limit of proportion of 1's in binary expansion of $x$ does not exist has measure zero?

score 438 · Answer 6 · 2026-04-17 12:36:04

438

Views

The dual of the space of $p$-locally integrable functions

Published on 17 Apr 2026 - 12:36

score 632 · Answer 7 · 2026-04-13 09:49:44

632

Views

Is the outer measure of $[0, 1] $ equal to $0$?

Published on 13 Apr 2026 - 9:49

score 520 · Answer 8 · 2026-04-11 22:13:51

520

Views

Differentiation under the integral sign when derivative exists only almost everywhere

Published on 11 Apr 2026 - 22:13

score 1.8k · Answer 9 · 2026-04-16 07:28:20

1.8k

Views

If $\mathcal{B}$ is a base of a topology space $\left(X,\tau\right)$, then the Borel $\sigma$-algebra is generated by $\mathcal{B}$?

Published on 16 Apr 2026 - 7:28

score 132 · Answer 10 · 2026-04-09 21:09:04

132

Views

Use DCT to show:

Published on 09 Apr 2026 - 21:09

score 575 · Answer 11 · 2026-04-24 13:05:08

575

Views

$\mu$ is a finite Borel measure on $\Bbb R$, absolutely continuous w.r.t. to the Lebesgue measure $m$. Prove that $x \mapsto \mu(A+x)$ is continuous.

Published on 24 Apr 2026 - 13:05

score 206 · Answer 12 · 2026-04-24 12:59:11

206

Views

Can this be proved using the MCT instead of the DCT?

Published on 24 Apr 2026 - 12:59

score 434 · Answer 13 · 2026-04-14 07:15:47

434

Views

Looking for a bounded set in a set with finite measure lebesgue.

Published on 14 Apr 2026 - 7:15

score 1k · Answer 14 · 2026-04-13 10:15:27

1k

Views

Subset of null set (set of measure zero)

Published on 13 Apr 2026 - 10:15

score 494 · Answer 15 · 2026-04-15 07:27:30

494

Views

Show that the image of Lipschitz function $\gamma : [0,1] \to R^n$ has measure $0$, if $n \ge 2$.

Published on 15 Apr 2026 - 7:27

List Question

Is $\overline{D}_{\varepsilon}$ a connected Jordan region in $\mathbb{R}^{n}?$

Sets cut into two halves of equal size by any straight line through a particular point

Can we find uncountably many disjoint dense measurable uncountable subsets of $[0,1]$?

Is the intersection of the following closed and open set closed? Generally?

Is there an easy proof that the set of $x \in [0,1]$ whose limit of proportion of 1's in binary expansion of $x$ does not exist has measure zero?

The dual of the space of $p$-locally integrable functions

Is the outer measure of $[0, 1] $ equal to $0$?

Differentiation under the integral sign when derivative exists only almost everywhere

If $\mathcal{B}$ is a base of a topology space $\left(X,\tau\right)$, then the Borel $\sigma$-algebra is generated by $\mathcal{B}$?

Use DCT to show:

$\mu$ is a finite Borel measure on $\Bbb R$, absolutely continuous w.r.t. to the Lebesgue measure $m$. Prove that $x \mapsto \mu(A+x)$ is continuous.

Can this be proved using the MCT instead of the DCT?

Looking for a bounded set in a set with finite measure lebesgue.

Subset of null set (set of measure zero)

Show that the image of Lipschitz function $\gamma : [0,1] \to R^n$ has measure $0$, if $n \ge 2$.

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