Question

Can every subset of $\mathbb{R}$ a measurable set (with respect to some measure $\mu$)?

score 45 · Answer 1 · 2026-04-11 21:47:01

45

Views

Can every subset of $\mathbb{R}$ a measurable set (with respect to some measure $\mu$)?

Published on 11 Apr 2026 - 21:47

score 60 · Answer 2 · 2026-04-11 10:16:53

60

Views

Continuous Almost Everywhere Implies Measurability

Published on 11 Apr 2026 - 10:16

score 169 · Answer 3 · 2026-04-17 06:50:32

169

Views

If $\int_a^b f(x) \ dx > 0$ then $f(x) > 0$ a.e?

Published on 17 Apr 2026 - 6:50

score 49 · Answer 4 · 2026-04-09 09:57:06

49

Views

Is it possible that a set be measurable with a measure function but not with the other?

Published on 09 Apr 2026 - 9:57

score 89 · Answer 5 · 2026-04-10 06:12:37

89

Views

Additivity of outer measure when one set is closed (Axler: Measure, Integration & Real Analysis)

Published on 10 Apr 2026 - 6:12

score 67 · Answer 6 · 2026-04-11 04:51:47

67

Views

Nearly covering the complement of a nowhere dense set

Published on 11 Apr 2026 - 4:51

score 57 · Answer 7 · 2026-04-14 11:02:50

57

Views

Verifying the countably additive measure property of $\nu_f$ when $\nu_f(E)$ is infinite

Published on 14 Apr 2026 - 11:02

score 192 · Answer 8 · 2026-04-15 04:30:07

192

Views

$\int_0^1 x^n f(x)\,\mathrm{d}x = 0$ for all $n$ implies $f=0$ almost everywhere

Published on 15 Apr 2026 - 4:30

score 26 · Answer 9 · 2026-04-13 06:50:26

26

Views

Show that the image of a homeomorphism involving the Cantor function has a certain measure

Published on 13 Apr 2026 - 6:50

score 48 · Answer 10 · 2026-04-17 01:42:23

48

Views

There is a function $f$ such that $f \in L^{p}$ and $f \notin L^{q}$ for $p,q \geq 1$ and $p\neq q$

Published on 17 Apr 2026 - 1:42

score 50 · Answer 11 · 2026-03-25 21:48:12

50

Views

Subset $V$ Lebesgue measurable, but not Borel measurable

Published on 25 Mar 2026 - 21:48

score 60 · Answer 12 · 2026-04-13 06:10:40

60

Views

A question related to a signed measure on the real numbers

Published on 13 Apr 2026 - 6:10

score 65 · Answer 13 · 2026-04-17 11:02:47

65

Views

Let $f:[0,1]\mapsto [0,\infty]$ be a bounded, measurable function, prove that $\int_{[0,1]} f\text { }dm=\inf\int_{[0,1]} \phi\text { }dm$

Published on 17 Apr 2026 - 11:02

score 88 · Answer 14 · 2026-04-16 18:02:15

88

Views

Looking for a non-$\sigma$-finite measure for a counter example

Published on 16 Apr 2026 - 18:02

score 63 · Answer 15 · 2026-04-15 23:22:38

63

Views

If $m(A)=0$, does this imply that $m(\log(A)) = 0$ when $A\subset \mathbb{R}_{+}$

Published on 15 Apr 2026 - 23:22

List Question

Can every subset of $\mathbb{R}$ a measurable set (with respect to some measure $\mu$)?

Continuous Almost Everywhere Implies Measurability

If $\int_a^b f(x) \ dx > 0$ then $f(x) > 0$ a.e?

Is it possible that a set be measurable with a measure function but not with the other?

Additivity of outer measure when one set is closed (Axler: Measure, Integration & Real Analysis)

Nearly covering the complement of a nowhere dense set

Verifying the countably additive measure property of $\nu_f$ when $\nu_f(E)$ is infinite

$\int_0^1 x^n f(x)\,\mathrm{d}x = 0$ for all $n$ implies $f=0$ almost everywhere

Show that the image of a homeomorphism involving the Cantor function has a certain measure

There is a function $f$ such that $f \in L^{p}$ and $f \notin L^{q}$ for $p,q \geq 1$ and $p\neq q$

Subset $V$ Lebesgue measurable, but not Borel measurable

A question related to a signed measure on the real numbers

Let $f:[0,1]\mapsto [0,\infty]$ be a bounded, measurable function, prove that $\int_{[0,1]} f\text { }dm=\inf\int_{[0,1]} \phi\text { }dm$

Looking for a non-$\sigma$-finite measure for a counter example

If $m(A)=0$, does this imply that $m(\log(A)) = 0$ when $A\subset \mathbb{R}_{+}$

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