Question

show that $cf$ is Lebesgue integrable

score 398 · Answer 1 · 2026-04-16 06:41:05

398

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show that $cf$ is Lebesgue integrable

Published on 16 Apr 2026 - 6:41

score 150 · Answer 2 · 2026-04-14 08:51:37

150

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In the Littlewood’s 1st Principle, why do we need the finiteness assumption m∗ (E) < ∞?

Published on 14 Apr 2026 - 8:51

score 90 · Answer 3 · 2026-04-14 08:53:06

90

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Assume that $\|f\|_p\leq C$ for all $p\geq1$ show that $f \in L^\infty [0,1]$ [proof verificatoin]

Published on 14 Apr 2026 - 8:53

score 55 · Answer 4 · 2026-04-15 04:12:06

55

Views

Show that $f$ is measurable in $\Bbb R\ \iff$ the set $\{(x,y), f(x)>y\}$ is measurable in $\Bbb R^2$

Published on 15 Apr 2026 - 4:12

score 109 · Answer 5 · 2026-04-16 04:20:19

109

Views

I want to prove or disprove "∀ open interval I, m∗(I) = m∗(I∩E)+m∗(I∩E^c)" implies "E is lebesgue measurable".

Published on 16 Apr 2026 - 4:20

score 124 · Answer 6 · 2026-04-11 02:32:17

124

Views

Property of Lebesgue integrable function proof verification

Published on 11 Apr 2026 - 2:32

score 60 · Answer 7 · 2026-04-12 10:39:38

60

Views

Proving the existence of a subset, given the Lebesgue outer measure

Published on 12 Apr 2026 - 10:39

score 99 · Answer 8 · 2026-04-12 14:36:25

99

Views

Lebesgue density, but not sigma finite

Published on 12 Apr 2026 - 14:36

score 125 · Answer 9 · 2026-04-14 03:54:20

125

Views

Borel set invariant under certain translation must have zero or full measure

Published on 14 Apr 2026 - 3:54

score 60 · Answer 10 · 2026-04-12 03:08:08

60

Views

I have a question on Lebesgue Integral Properties

Published on 12 Apr 2026 - 3:08

score 290 · Answer 11 · 2026-04-10 12:01:50

290

Views

Absolute value of integral equal to integral of absolute value

Published on 10 Apr 2026 - 12:01

score 624 · Answer 12 · 2026-03-28 22:36:52

624

Views

Real Analysis, Folland Exercise 1.5.33 Borel measures on the real line

Published on 28 Mar 2026 - 22:36

score 206 · Answer 13 · 2026-04-15 07:04:40

206

Views

Show g is integrable if and only if $\sum_{k = 0}^{\infty} 3^{k} \lambda(C_k) < \infty$

Published on 15 Apr 2026 - 7:04

score 286 · Answer 14 · 2026-04-14 16:35:02

286

Views

Proving that set $Z = \{(x,y) : F (x, y) = 0\}$ has measure $0$

Published on 14 Apr 2026 - 16:35

score 106 · Answer 15 · 2026-04-10 21:07:44

106

Views

understand about Egorov's Theorem

Published on 10 Apr 2026 - 21:07

List Question

show that $cf$ is Lebesgue integrable

In the Littlewood’s 1st Principle, why do we need the finiteness assumption m∗ (E) < ∞?

Assume that $\|f\|_p\leq C$ for all $p\geq1$ show that $f \in L^\infty [0,1]$ [proof verificatoin]

Show that $f$ is measurable in $\Bbb R\ \iff$ the set $\{(x,y), f(x)>y\}$ is measurable in $\Bbb R^2$

I want to prove or disprove "∀ open interval I, m∗(I) = m∗(I∩E)+m∗(I∩E^c)" implies "E is lebesgue measurable".

Property of Lebesgue integrable function proof verification

Proving the existence of a subset, given the Lebesgue outer measure

Lebesgue density, but not sigma finite

Borel set invariant under certain translation must have zero or full measure

I have a question on Lebesgue Integral Properties

Absolute value of integral equal to integral of absolute value

Real Analysis, Folland Exercise 1.5.33 Borel measures on the real line

Show g is integrable if and only if $\sum_{k = 0}^{\infty} 3^{k} \lambda(C_k) < \infty$

Proving that set $Z = \{(x,y) : F (x, y) = 0\}$ has measure $0$

understand about Egorov's Theorem

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