Question

Use the definition of the integral to prove that if $A \subset E$, where $E$ is measurable, then $\int_A f = \int_E f \chi_{A}$

score 929 · Answer 1 · 2026-04-27 17:11:47

929

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Use the definition of the integral to prove that if $A \subset E$, where $E$ is measurable, then $\int_A f = \int_E f \chi_{A}$

Published on 27 Apr 2026 - 17:11

score 89 · Answer 2 · 2026-03-31 11:50:44

89

Views

Average of decimal digits

Published on 31 Mar 2026 - 11:50

score 36 · Answer 3 · 2026-04-12 23:08:43

36

Views

Show that retarded argument functional operator is surjective

Published on 12 Apr 2026 - 23:08

score 499 · Answer 4 · 2026-03-27 14:49:24

499

Views

Difference of increasing functions differentiable a.e.

Published on 27 Mar 2026 - 14:49

score 335 · Answer 5 · 2026-04-10 01:52:33

335

Views

Problem on Lebesgue differentiation theorem

Published on 10 Apr 2026 - 1:52

score 51 · Answer 6 · 2026-03-27 16:21:48

51

Views

Under Given conditions, is f absolutely continuous on $[0,1]$?

Published on 27 Mar 2026 - 16:21

score 156 · Answer 7 · 2026-04-12 21:41:02

156

Views

Limit of an integral that resembles the Riemann-Lebesgue Lemma

Published on 12 Apr 2026 - 21:41

score 64 · Answer 8 · 2026-04-14 01:17:11

64

Views

any countereample in measurable function

Published on 14 Apr 2026 - 1:17

score 828 · Answer 9 · 2026-04-17 15:50:27

828

Views

Bounded Sequence in $L^p$ is Tight

Published on 17 Apr 2026 - 15:50

score 168 · Answer 10 · 2026-04-27 18:31:47

168

Views

Prove that if E is positive lebesgue measurabel set, then E − E and E + E contain non-empty open sets.

Published on 27 Apr 2026 - 18:31

score 311 · Answer 11 · 2026-04-27 18:32:49

311

Views

Measure of boundary in $\mathbb R^n$

Published on 27 Apr 2026 - 18:32

score 180 · Answer 12 · 2026-04-15 12:40:09

180

Views

Let $E$ be a measurable set and let $g$ be a function defined on $E$. The product $fg$ belongs to $L^1(E)$ for every function $f \in L^1(E)$

Published on 15 Apr 2026 - 12:40

score 223 · Answer 13 · 2026-04-29 23:50:50

223

Views

Is the set obtained by removing intervals of $1/4^n$ a borel set?

Published on 29 Apr 2026 - 23:50

score 60 · Answer 14 · 2026-05-04 10:09:59

60

Views

Can someone clarify in simple terms what it means to "apply an inequality to a measure"?

Published on 04 May 2026 - 10:09

score 947 · Answer 15 · 2026-04-27 18:32:02

947

Views

Show that measure of symmetric difference $= \int_{E}\vert \chi_{A} - \chi_{B}\vert$

Published on 27 Apr 2026 - 18:32

List Question

Use the definition of the integral to prove that if $A \subset E$, where $E$ is measurable, then $\int_A f = \int_E f \chi_{A}$

Average of decimal digits

Show that retarded argument functional operator is surjective

Difference of increasing functions differentiable a.e.

Problem on Lebesgue differentiation theorem

Under Given conditions, is f absolutely continuous on $[0,1]$?

Limit of an integral that resembles the Riemann-Lebesgue Lemma

any countereample in measurable function

Bounded Sequence in $L^p$ is Tight

Prove that if E is positive lebesgue measurabel set, then E − E and E + E contain non-empty open sets.

Measure of boundary in $\mathbb R^n$

Let $E$ be a measurable set and let $g$ be a function defined on $E$. The product $fg$ belongs to $L^1(E)$ for every function $f \in L^1(E)$

Is the set obtained by removing intervals of $1/4^n$ a borel set?

Can someone clarify in simple terms what it means to "apply an inequality to a measure"?

Show that measure of symmetric difference $= \int_{E}\vert \chi_{A} - \chi_{B}\vert$

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