Question

Does this proof of convergence work?

score 67 · Answer 1 · 2021-05-25 17:17:54

67

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Does this proof of convergence work?

Published on 25 May 2021 - 17:17

score 80 · Answer 2 · 2021-05-25 20:14:24

80

Views

Question integral

Published on 25 May 2021 - 20:14

score 470 · Answer 3 · 2026-03-31 03:39:03

470

Views

Proving that the set of real numbers with digit 5 appearing infinitely often is Borel by using a Borel measurable function

Published on 31 Mar 2026 - 3:39

score 885 · Answer 4 · 2021-05-30 21:26:02

885

Views

Let $f : \mathbb{R} \to \mathbb{R}$ be measurable and let $Z = {\{x : f'(x)=0}\}$. Prove that $λ(f(Z)) = 0$.

Published on 30 May 2021 - 21:26

score 130 · Answer 5 · 2021-06-01 05:27:41

130

Views

Why $f$ is Lebesgue-measurable? $f_n\to f$ almost everywhere.

Published on 01 Jun 2021 - 5:27

score 50 · Answer 6 · 2026-03-26 09:41:52

50

Views

If $A_n=\{x\in \mathbb{R}:f(x)<\frac{-1}{n}\}$ are measurable, prove that $A=\{x\in \mathbb{R}:f(x)\le0\}$ is measurable too.

Published on 26 Mar 2026 - 9:41

score 258 · Answer 7 · 2021-06-05 20:47:26

258

Views

Prob. 1, Chap. 3, in Royden's REAL ANALYSIS: If continuous functions $f$ and $g$ agree a.e. on $[a,b]$, then $f=g$ on $[a,b]$

Published on 05 Jun 2021 - 20:47

score 75 · Answer 8 · 2021-06-07 03:16:08

75

Views

Are Lebesgue integral definitions equivalent for nonnegative bounded functions on finite support?

Published on 07 Jun 2021 - 3:16

score 74 · Answer 9 · 2021-06-08 20:19:45

74

Views

Measurability in Linear Regressions

Published on 08 Jun 2021 - 20:19

score 54 · Answer 10 · 2021-06-08 23:42:31

54

Views

Why is the reverse image $\Phi^{-1}$ Lebesgue-measurable?

Published on 08 Jun 2021 - 23:42

score 473 · Answer 11 · 2026-03-31 05:42:39

473

Views

A real valued function defined on a Borel subset of $\mathbb{R}$ with a countable number of discontinuities is Borel measurable

Published on 31 Mar 2026 - 5:42

score 63 · Answer 12 · 2026-03-26 12:37:22

63

Views

If non negative functions $f,g : \mathbb{R^n} \to [0, \infty]$ are measurable, then $f+g$ is measurable.

Published on 26 Mar 2026 - 12:37

score 42 · Answer 13 · 2026-03-26 11:01:35

42

Views

Proof of the fact that $\{ x \in \mathbb{R^n} | f(x)\neq g(x) \}$ is lebesgue-measurable.

Published on 26 Mar 2026 - 11:01

score 238 · Answer 14 · 2026-03-26 11:01:34

238

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$f,g$ are lebesgue-measurable and finite a.e. Then, prove that $f\cdot g$ is lebesgue-measurable.

Published on 26 Mar 2026 - 11:01

score 16 · Answer 15 · 2021-06-14 12:04:24

What can be said about the measurability of $f(x,\cdot):Y\to\mathbb{R}$ if $f:X\times Y\to\mathbb{R}$ is not measurable?

List Question

Does this proof of convergence work?

Question integral

Proving that the set of real numbers with digit 5 appearing infinitely often is Borel by using a Borel measurable function

Let $f : \mathbb{R} \to \mathbb{R}$ be measurable and let $Z = {\{x : f'(x)=0}\}$. Prove that $λ(f(Z)) = 0$.

Why $f$ is Lebesgue-measurable? $f_n\to f$ almost everywhere.

If $A_n=\{x\in \mathbb{R}:f(x)<\frac{-1}{n}\}$ are measurable, prove that $A=\{x\in \mathbb{R}:f(x)\le0\}$ is measurable too.

Prob. 1, Chap. 3, in Royden's REAL ANALYSIS: If continuous functions $f$ and $g$ agree a.e. on $[a,b]$, then $f=g$ on $[a,b]$

Are Lebesgue integral definitions equivalent for nonnegative bounded functions on finite support?

Measurability in Linear Regressions

Why is the reverse image $\Phi^{-1}$ Lebesgue-measurable?

A real valued function defined on a Borel subset of $\mathbb{R}$ with a countable number of discontinuities is Borel measurable

If non negative functions $f,g : \mathbb{R^n} \to [0, \infty]$ are measurable, then $f+g$ is measurable.

Proof of the fact that $\{ x \in \mathbb{R^n} | f(x)\neq g(x) \}$ is lebesgue-measurable.

$f,g$ are lebesgue-measurable and finite a.e. Then, prove that $f\cdot g$ is lebesgue-measurable.

What can be said about the measurability of $f(x,\cdot):Y\to\mathbb{R}$ if $f:X\times Y\to\mathbb{R}$ is not measurable?

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