Question

Is it possible to show that an absolutely continuous function $I\to \mathbb{R}$ is differentiable a.e. without invoking Lebesgue theory?

score 100 · Answer 1 · 2026-04-13 01:11:27

100

Views

Is it possible to show that an absolutely continuous function $I\to \mathbb{R}$ is differentiable a.e. without invoking Lebesgue theory?

Published on 13 Apr 2026 - 1:11

score 100 · Answer 2 · 2026-04-11 03:44:27

100

Views

How to prove the compound angle formula rigorously, starting only from the Taylor series definition

Published on 11 Apr 2026 - 3:44

score 125 · Answer 3 · 2026-04-14 09:34:27

125

Views

Ways to place regular polygons around a planar vertex

Published on 14 Apr 2026 - 9:34

score 59 · Answer 4 · 2026-04-11 19:08:56

59

Views

Proof of the Peano existence theorem using a sequence of piecewise linear functions

Published on 11 Apr 2026 - 19:08

score 67 · Answer 5 · 2026-04-11 19:34:27

67

Views

Cauchy–Kowalevski theorem: proof by direct estimate rather than analytic majorization

Published on 11 Apr 2026 - 19:34

score 48 · Answer 6 · 2026-04-16 13:09:24

48

Views

Prove or disprove: Let k ∈ N. If $k^2 + 5k$ is odd, then $(k + 1)^2$ + 5(k + 1) is odd.

Published on 16 Apr 2026 - 13:09

score 154 · Answer 7 · 2026-04-09 22:15:42

154

Views

Is there any better way of finding the required value

Published on 09 Apr 2026 - 22:15

score 196 · Answer 8 · 2026-04-12 20:32:39

196

Views

Show that the equation $x^4-8x^3+22x^2-24x+4=0$ has exactly two real roots, both being positive

Published on 12 Apr 2026 - 20:32

score 329 · Answer 9 · 2026-04-14 20:09:07

329

Views

Can Carathéodory's Extension Lemma be proven without use of the Carathéodory's Restriction Lemma?

Published on 14 Apr 2026 - 20:09

score 43 · Answer 10 · 2026-04-10 20:18:15

43

Views

Exercise 7, Section 6.2 of Hoffman’s Linear Algebra

Published on 10 Apr 2026 - 20:18

score 59 · Answer 11 · 2026-04-18 14:25:23

59

Views

$E$(hits) if for every fail, you divide the probability of hitting by $C$, and for each hit, you divide the probability of failing by $C$?

Published on 18 Apr 2026 - 14:25

score 438 · Answer 12 · 2026-04-15 06:15:40

438

Views

Showing that $H=M\oplus M^{\perp}$ provided that $M$ is closed and $H$ is Hilbert space.

Published on 15 Apr 2026 - 6:15

score 224 · Answer 13 · 2026-04-16 05:26:19

224

Views

Proof that $\frac{(1+\sqrt 5)^n+(1-\sqrt 5)^n}{2^n}$ is an integer

Published on 16 Apr 2026 - 5:26

score 90 · Answer 14 · 2026-04-08 16:59:27

90

Views

alternate proof of fixed point theorem

Published on 08 Apr 2026 - 16:59

score 102 · Answer 15 · 2026-04-10 23:00:42

102

Views

Showing that the image of an integral operator is continuous on a compact interval

Published on 10 Apr 2026 - 23:00

List Question

Is it possible to show that an absolutely continuous function $I\to \mathbb{R}$ is differentiable a.e. without invoking Lebesgue theory?

How to prove the compound angle formula rigorously, starting only from the Taylor series definition

Ways to place regular polygons around a planar vertex

Proof of the Peano existence theorem using a sequence of piecewise linear functions

Cauchy–Kowalevski theorem: proof by direct estimate rather than analytic majorization

Prove or disprove: Let k ∈ N. If $k^2 + 5k$ is odd, then $(k + 1)^2$ + 5(k + 1) is odd.

Is there any better way of finding the required value

Show that the equation $x^4-8x^3+22x^2-24x+4=0$ has exactly two real roots, both being positive

Can Carathéodory's Extension Lemma be proven without use of the Carathéodory's Restriction Lemma?

Exercise 7, Section 6.2 of Hoffman’s Linear Algebra

$E$(hits) if for every fail, you divide the probability of hitting by $C$, and for each hit, you divide the probability of failing by $C$?

Showing that $H=M\oplus M^{\perp}$ provided that $M$ is closed and $H$ is Hilbert space.

Proof that $\frac{(1+\sqrt 5)^n+(1-\sqrt 5)^n}{2^n}$ is an integer

alternate proof of fixed point theorem

Showing that the image of an integral operator is continuous on a compact interval

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