Question

The function defined with the Lebesgue's measure is measurable

score 56 · Answer 1 · 2026-04-12 20:53:48

56

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The function defined with the Lebesgue's measure is measurable

Published on 12 Apr 2026 - 20:53

score 100 · Answer 2 · 2026-04-14 04:58:17

100

Views

Construct a sequence of simple functions converging to $f\in C([a,b])$

Published on 14 Apr 2026 - 4:58

score 89 · Answer 3 · 2026-04-10 05:25:41

89

Views

An exercise of measure theory is probably wrong?

Published on 10 Apr 2026 - 5:25

score 236 · Answer 4 · 2026-04-11 01:32:44

236

Views

spectral gap of an operator

Published on 11 Apr 2026 - 1:32

score 186 · Answer 5 · 2026-04-13 18:21:42

186

Views

Weak convergence of a sequence of probability measures implies integrability of the limiting probability measure

Published on 13 Apr 2026 - 18:21

score 518 · Answer 6 · 2026-03-25 04:42:48

518

Views

Show Hausdorff measure $H^d$ on $R^n$ is not $\sigma$-finite if d<n

Published on 25 Mar 2026 - 4:42

score 249 · Answer 7 · 2026-04-20 10:36:10

249

Views

Prove $(X_n, F_n) $ Martingale $\iff \int_{F} X_{n+1} = \int_{F} X_{n} \forall F \in F_n$

Published on 20 Apr 2026 - 10:36

score 91 · Answer 8 · 2026-04-14 22:58:56

91

Views

Prove that there is a unique probability on $[0,1]$ s.t. $\mathbb P([0,x])=x$.

Published on 14 Apr 2026 - 22:58

score 46 · Answer 9 · 2026-04-17 05:50:16

46

Views

What does $\limsup_{r \to 0} r^{-p}⨍_{B(x_0,r)} f^{q}(x) dx < \infty $ imply on the behavior of $f$?

Published on 17 Apr 2026 - 5:50

score 175 · Answer 10 · 2026-04-14 01:36:02

175

Views

What if we weaken this hypothesis? Folland's real analysis Theorem 6.18

Published on 14 Apr 2026 - 1:36

score 1.4k · Answer 11 · 2026-04-13 22:40:02

1.4k

Views

Limit of $L^p$ Norms and Essential Supremum

Published on 13 Apr 2026 - 22:40

score 34 · Answer 12 · 2026-04-14 20:43:31

34

Views

Does there exist a Lebesgue measurable set $[0,1] \subset D$ such that $D \neq [0,1]$ and $\lambda ^{*} (D) = 1$?

Published on 14 Apr 2026 - 20:43

score 172 · Answer 13 · 2026-04-12 04:27:11

172

Views

Two $\sigma$-finite measures on an algebra are unique; monotone class form.

Published on 12 Apr 2026 - 4:27

score 91 · Answer 14 · 2026-04-11 06:20:19

91

Views

Equality between volume and surface

Published on 11 Apr 2026 - 6:20

score 449 · Answer 15 · 2026-04-20 14:12:53

449

Views

Haar measure of $p$-adic integers with valuation 0 modulo 3

Published on 20 Apr 2026 - 14:12

List Question

The function defined with the Lebesgue's measure is measurable

Construct a sequence of simple functions converging to $f\in C([a,b])$

An exercise of measure theory is probably wrong?

spectral gap of an operator

Weak convergence of a sequence of probability measures implies integrability of the limiting probability measure

Show Hausdorff measure $H^d$ on $R^n$ is not $\sigma$-finite if d<n

Prove $(X_n, F_n) $ Martingale $\iff \int_{F} X_{n+1} = \int_{F} X_{n} \forall F \in F_n$

Prove that there is a unique probability on $[0,1]$ s.t. $\mathbb P([0,x])=x$.

What does $\limsup_{r \to 0} r^{-p}⨍_{B(x_0,r)} f^{q}(x) dx < \infty $ imply on the behavior of $f$?

What if we weaken this hypothesis? Folland's real analysis Theorem 6.18

Limit of $L^p$ Norms and Essential Supremum

Does there exist a Lebesgue measurable set $[0,1] \subset D$ such that $D \neq [0,1]$ and $\lambda ^{*} (D) = 1$?

Two $\sigma$-finite measures on an algebra are unique; monotone class form.

Equality between volume and surface

Haar measure of $p$-adic integers with valuation 0 modulo 3

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