Question

$\pi-\lambda$ Theorem to show measure giving interval lengths equivalent to Lebesgue on [0,1]

score 266 · Answer 1 · 2026-04-17 04:24:37

266

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$\pi-\lambda$ Theorem to show measure giving interval lengths equivalent to Lebesgue on [0,1]

Published on 17 Apr 2026 - 4:24

score 380 · Answer 2 · 2026-04-13 17:06:13

380

Views

Dunford Pettis Theorem

Published on 13 Apr 2026 - 17:06

score 284 · Answer 3 · 2026-04-23 21:31:45

284

Views

A weaker form of Lebesgue's differentiation theorem in $\Bbb R ^n$

Published on 23 Apr 2026 - 21:31

score 78 · Answer 4 · 2026-04-12 10:43:41

78

Views

Is $L^p(\Omega) = L^p(\bar {\Omega})$?

Published on 12 Apr 2026 - 10:43

score 420 · Answer 5 · 2026-04-12 22:43:58

420

Views

Lebesgue Measure of Image of Unit Square under Continuous Map

Published on 12 Apr 2026 - 22:43

score 5.7k · Answer 6 · 2026-04-24 01:11:16

5.7k

Views

for each $\epsilon >0$ there is a $\delta >0$ such that whenever $m(A)<\delta$, $\int_A f(x)dx <\epsilon$

Published on 24 Apr 2026 - 1:11

score 412 · Answer 7 · 2026-04-13 05:26:08

412

Views

lebesgue measure basic exercise

Published on 13 Apr 2026 - 5:26

score 258 · Answer 8 · 2026-04-16 02:43:56

258

Views

Prove that $\lim\limits_{n \to \infty } \int_0^\infty (1 + x/n)^{-n}x^{-1/n}dx= 1$ using DCT

Published on 16 Apr 2026 - 2:43

score 380 · Answer 9 · 2026-04-17 07:16:27

380

Views

If $A_1 \subset A_2 \subset \mathbb R$ and $m^(A_1) = m^(A_2)$, will $m^(A_1 \cap T) = m^(A_2 \cap T), \forall T \subset \mathbb R$?

Published on 17 Apr 2026 - 7:16

score 68 · Answer 10 · 2026-04-11 21:13:06

68

Views

Outer measure exclusion of zero set

Published on 11 Apr 2026 - 21:13

score 1.2k · Answer 11 · 2026-04-16 08:25:34

1.2k

Views

Subsets $B$ of bounded subinterval $I$ is lebesgue measurable iff $\lambda^(I)=\lambda^(B)+\lambda^*(I\cap B^c)$

Published on 16 Apr 2026 - 8:25

score 533 · Answer 12 · 2026-04-16 01:12:47

533

Views

Absolutely Continuous Weakly Convergent Sequence Need Not Converge Strongly

Published on 16 Apr 2026 - 1:12

score 149 · Answer 13 · 2026-04-12 02:59:42

149

Views

Is the product $d x \otimes \mu_x(d y)$ on $[0,1] \times [0,1]$ a probability measure?

Published on 12 Apr 2026 - 2:59

score 74 · Answer 14 · 2026-04-13 21:39:48

74

Views

Characterize the $\mu^$- measurable sets where $\mu^∗ = \lambda^ \circ \text{proj}_1 $ and $ \lambda^*$ is the Lebesgue outer measure

Published on 13 Apr 2026 - 21:39

score 73 · Answer 15 · 2026-04-24 01:05:55

73

Views

Prove continuity of averaging function for integrable $f$

Published on 24 Apr 2026 - 1:05

List Question

$\pi-\lambda$ Theorem to show measure giving interval lengths equivalent to Lebesgue on [0,1]

Dunford Pettis Theorem

A weaker form of Lebesgue's differentiation theorem in $\Bbb R ^n$

Is $L^p(\Omega) = L^p(\bar {\Omega})$?

Lebesgue Measure of Image of Unit Square under Continuous Map

for each $\epsilon >0$ there is a $\delta >0$ such that whenever $m(A)<\delta$, $\int_A f(x)dx <\epsilon$

lebesgue measure basic exercise

Prove that $\lim\limits_{n \to \infty } \int_0^\infty (1 + x/n)^{-n}x^{-1/n}dx= 1$ using DCT

If $A_1 \subset A_2 \subset \mathbb R$ and $m^(A_1) = m^(A_2)$, will $m^(A_1 \cap T) = m^(A_2 \cap T), \forall T \subset \mathbb R$?

Outer measure exclusion of zero set

Subsets $B$ of bounded subinterval $I$ is lebesgue measurable iff $\lambda^(I)=\lambda^(B)+\lambda^*(I\cap B^c)$

Absolutely Continuous Weakly Convergent Sequence Need Not Converge Strongly

Is the product $d x \otimes \mu_x(d y)$ on $[0,1] \times [0,1]$ a probability measure?

Characterize the $\mu^$- measurable sets where $\mu^∗ = \lambda^ \circ \text{proj}_1 $ and $ \lambda^*$ is the Lebesgue outer measure

Prove continuity of averaging function for integrable $f$

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