Question

Show that the set of all real numbers whose decimal notation includes the number 2 are borel measurable

score 728 · Answer 1 · 2026-03-28 08:35:39

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Show that the set of all real numbers whose decimal notation includes the number 2 are borel measurable

Published on 28 Mar 2026 - 8:35

score 197 · Answer 2 · 2017-10-30 02:55:22

197

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$\sigma$-Algebra, Borel sets, Borel $\sigma$-Algebra

Published on 30 Oct 2017 - 2:55

score 35 · Answer 3 · 2017-10-30 15:15:29

35

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Show that $\int_{[a,b]}f(x)d\mu (x) = \int_a^b f(x)d\alpha (x)$ where $\mu$ is final non-negative measure on Borel sets on $[a,b]$.

Published on 30 Oct 2017 - 15:15

score 74 · Answer 4 · 2026-03-28 08:35:39

74

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$A_n\downarrow A \implies \mu(A_n) \downarrow \mu(A)$ need not be true when $\mu(A_1) = \infty$

Published on 28 Mar 2026 - 8:35

score 46 · Answer 5 · 2017-10-31 18:33:50

46

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Show that this set $\{a_n\in\mathbb{R} : n\in\mathbb{N}\}$ has lebesgue measure zero.

Published on 31 Oct 2017 - 18:33

score 158 · Answer 6 · 2017-10-31 19:17:23

158

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Let $m(\partial A)=0$, show that $A$ is Lebesgue measurable

Published on 31 Oct 2017 - 19:17

score 631 · Answer 7 · 2026-03-28 08:35:37

631

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If $E$ is a Borel measurable set, show that there exists a subset of $E$ with half measure.

Published on 28 Mar 2026 - 8:35

score 55 · Answer 8 · 2026-03-28 08:36:36

55

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Finding a non-measurable function

Published on 28 Mar 2026 - 8:36

score 136 · Answer 9 · 2017-11-04 06:00:25

136

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Defining random variable (notation).

Published on 04 Nov 2017 - 6:00

score 34 · Answer 10 · 2026-03-28 10:23:38

34

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Measurability of f, defining the right intervals.

Published on 28 Mar 2026 - 10:23

score 133 · Answer 11 · 2017-11-07 14:24:32

133

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Uncountable unions of disjoint sets and the corresponding $\sigma$-algebras

Published on 07 Nov 2017 - 14:24

score 1.7k · Answer 12 · 2017-11-08 01:53:46

1.7k

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Cartesian product of two Borel sets is a Borel Set

Published on 08 Nov 2017 - 1:53

score 386 · Answer 13 · 2017-11-08 16:51:20

386

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Borel measure of point is 1

Published on 08 Nov 2017 - 16:51

score 377 · Answer 14 · 2026-03-28 08:38:23

377

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Borel $\sigma$-algebra generated by pseudo base

Published on 28 Mar 2026 - 8:38

score 683 · Answer 15 · 2017-11-17 02:54:32

683

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If $f^3$ measurable, show $f$ is measurable (Check my solution please)

Published on 17 Nov 2017 - 2:54

List Question

Show that the set of all real numbers whose decimal notation includes the number 2 are borel measurable

$\sigma$-Algebra, Borel sets, Borel $\sigma$-Algebra

Show that $\int_{[a,b]}f(x)d\mu (x) = \int_a^b f(x)d\alpha (x)$ where $\mu$ is final non-negative measure on Borel sets on $[a,b]$.

$A_n\downarrow A \implies \mu(A_n) \downarrow \mu(A)$ need not be true when $\mu(A_1) = \infty$

Show that this set $\{a_n\in\mathbb{R} : n\in\mathbb{N}\}$ has lebesgue measure zero.

Let $m(\partial A)=0$, show that $A$ is Lebesgue measurable

If $E$ is a Borel measurable set, show that there exists a subset of $E$ with half measure.

Finding a non-measurable function

Defining random variable (notation).

Measurability of f, defining the right intervals.

Uncountable unions of disjoint sets and the corresponding $\sigma$-algebras

Cartesian product of two Borel sets is a Borel Set

Borel measure of point is 1

Borel $\sigma$-algebra generated by pseudo base

If $f^3$ measurable, show $f$ is measurable (Check my solution please)

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