Question

Clarification on a construction of a set $E \subset I$ intersecting every subinterval of $I$ with positive, non-full measure

score 187 · Answer 1 · 2026-04-12 09:21:27

187

Views

Clarification on a construction of a set $E \subset I$ intersecting every subinterval of $I$ with positive, non-full measure

Published on 12 Apr 2026 - 9:21

score 65 · Answer 2 · 2026-04-11 06:53:48

65

Views

Upper bound for the approximation of Lebesgue integral

Published on 11 Apr 2026 - 6:53

score 266 · Answer 3 · 2026-04-16 12:56:08

266

Views

Existence of {$s_n$}$\subset \mathbb R$ s.t. complement of $\cup_{n=1}^{\infty}(A+s_n)$ has measure zero

Published on 16 Apr 2026 - 12:56

score 131 · Answer 4 · 2026-04-13 18:30:59

131

Views

$\frac{1}{m(E)}\int _E f(x) dx\in S$ implies $f(x)\in S$ for a.e. $x$

Published on 13 Apr 2026 - 18:30

score 68 · Answer 5 · 2026-04-11 12:41:54

68

Views

Pythagorean theorem for Lebesgue measurable sets?

Published on 11 Apr 2026 - 12:41

score 49 · Answer 6 · 2026-04-15 17:30:17

49

Views

Reflection Property of the Lebesgue Integral

Published on 15 Apr 2026 - 17:30

score 49 · Answer 7 · 2026-04-17 08:15:59

49

Views

Show that $\int_E |f|^q \leq CN^{q/p} |E|^{1-q/p}$.

Published on 17 Apr 2026 - 8:15

score 58 · Answer 8 · 2026-04-15 23:44:08

58

Views

Lebesgue measure of the euclidean ball

Published on 15 Apr 2026 - 23:44

score 65 · Answer 9 · 2026-04-16 19:42:25

65

Views

Lebesgue integral preserves the inequality

Published on 16 Apr 2026 - 19:42

score 110 · Answer 10 · 2026-03-25 20:42:31

110

Views

Riemann-Stieltjes integral with respect to functions equal almost everywhere

Published on 25 Mar 2026 - 20:42

score 57 · Answer 11 · 2026-04-13 17:39:37

57

Views

Relation between boundedness of unit balls generated by a semi-norm and pseudo-Hermitian inner products dominated by the semi-norm

Published on 13 Apr 2026 - 17:39

score 32 · Answer 12 · 2026-04-17 14:19:46

32

Views

Let $E\subset \Bbb R^n$ be measurable, $mE>0$. and $0<p_0\neq q_0<\infty$, $L^{p_0}(E)\subset L^{q_0}(E)$. Show $q_0<p_0$.

Published on 17 Apr 2026 - 14:19

score 88 · Answer 13 · 2026-04-10 11:15:15

88

Views

Cantor Lebesgue theorem (Stein & Shakarchi Real Analysis problem)

Published on 10 Apr 2026 - 11:15

score 30 · Answer 14 · 2026-04-17 09:04:39

30

Views

Prove that $E(F(X))=\frac{1}{2}+\frac{1}{2}\sum_x[P(X=x)]^2$

Published on 17 Apr 2026 - 9:04

score 52 · Answer 15 · 2026-04-11 17:19:21

52

Views

If $f\in L^{1}([0,1]\times[0,1])$ and $F(x)=\int_{[0,x]\times[0,x]} f$ for$x\in [0,1]$, prove $F$ is absolutely continuous from the definition.

Published on 11 Apr 2026 - 17:19

List Question

Clarification on a construction of a set $E \subset I$ intersecting every subinterval of $I$ with positive, non-full measure

Upper bound for the approximation of Lebesgue integral

Existence of {$s_n$}$\subset \mathbb R$ s.t. complement of $\cup_{n=1}^{\infty}(A+s_n)$ has measure zero

$\frac{1}{m(E)}\int _E f(x) dx\in S$ implies $f(x)\in S$ for a.e. $x$

Pythagorean theorem for Lebesgue measurable sets?

Reflection Property of the Lebesgue Integral

Show that $\int_E |f|^q \leq CN^{q/p} |E|^{1-q/p}$.

Lebesgue measure of the euclidean ball

Lebesgue integral preserves the inequality

Riemann-Stieltjes integral with respect to functions equal almost everywhere

Relation between boundedness of unit balls generated by a semi-norm and pseudo-Hermitian inner products dominated by the semi-norm

Let $E\subset \Bbb R^n$ be measurable, $mE>0$. and $0<p_0\neq q_0<\infty$, $L^{p_0}(E)\subset L^{q_0}(E)$. Show $q_0<p_0$.

Cantor Lebesgue theorem (Stein & Shakarchi Real Analysis problem)

Prove that $E(F(X))=\frac{1}{2}+\frac{1}{2}\sum_x[P(X=x)]^2$

If $f\in L^{1}([0,1]\times[0,1])$ and $F(x)=\int_{[0,x]\times[0,x]} f$ for$x\in [0,1]$, prove $F$ is absolutely continuous from the definition.

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