Question

Prove that $\int_{X>\alpha}XdP\le\alpha(-\log F(\alpha))+\int_\alpha^\infty(-\log F(t))\lambda(dt)$

score 48 · Answer 1 · 2026-04-16 15:06:49

48

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Prove that $\int_{X>\alpha}XdP\le\alpha(-\log F(\alpha))+\int_\alpha^\infty(-\log F(t))\lambda(dt)$

Published on 16 Apr 2026 - 15:06

score 172 · Answer 2 · 2026-04-10 16:08:22

172

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Proving a set has Lebesgue measure zero

Published on 10 Apr 2026 - 16:08

score 56 · Answer 3 · 2026-03-25 23:37:43

56

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Relating an integral over a sphere to an integral of a sphere one dimension smaller "without" using polar coordinates

Published on 25 Mar 2026 - 23:37

score 131 · Answer 4 · 2026-03-25 23:11:03

131

Views

Show $\int _{0} ^{\infty} \frac{|f(x)|}{|x-a|^b} dx <\infty$ for a.e. $a\in \mathbb{R}$ if $f$ Lebesgue integrable on $\mathbb{R}$, $b\in (0,1)$

Published on 25 Mar 2026 - 23:11

score 49 · Answer 5 · 2026-04-15 09:48:11

49

Views

Using polar coordinates with radial functions in two variables

Published on 15 Apr 2026 - 9:48

score 120 · Answer 6 · 2026-04-09 07:33:35

120

Views

An application of Lusin's theorem.

Published on 09 Apr 2026 - 7:33

score 24 · Answer 7 · 2026-04-10 16:41:15

24

Views

Help in trying to understand a proof : Lebesgue outer measure as infimum of a Lebesgue Measure.

Published on 10 Apr 2026 - 16:41

score 127 · Answer 8 · 2026-04-11 15:03:42

127

Views

Measure of self-sums of a particular meager set of measure zero.

Published on 11 Apr 2026 - 15:03

score 56 · Answer 9 · 2026-04-14 01:31:43

56

Views

Proving Lebesgue integrability of a bounded function

Published on 14 Apr 2026 - 1:31

score 46 · Answer 10 · 2026-04-26 11:33:28

46

Views

Writing an integral over a sphere in terms of integrals of another spheres with lower dimension

Published on 26 Apr 2026 - 11:33

score 129 · Answer 11 · 2026-04-15 12:27:19

129

Views

Is it always true that $\int_{\Omega_n} f h\ dx = 0$ for any $h \in C_c (\Omega_n)$ eventually?

Published on 15 Apr 2026 - 12:27

score 48 · Answer 12 · 2026-04-09 13:58:45

48

Views

Which is better to use $A\leq B$ or $A=B$ in a proof of a proposition?

Published on 09 Apr 2026 - 13:58

score 130 · Answer 13 · 2026-04-15 23:05:49

130

Views

Equimeasurable functions of $p(\cdot) :[0;1] \to [1;\infty)$ and $p(\cdot\cdot) : [0;1]^2 \to [1; \infty)$.

Published on 15 Apr 2026 - 23:05

score 149 · Answer 14 · 2026-03-25 20:33:58

149

Views

Proper notation for integration on manifolds?

Published on 25 Mar 2026 - 20:33

score 68 · Answer 15 · 2026-04-12 15:48:51

68

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Distribution of a dense subset in an interval

Published on 12 Apr 2026 - 15:48

List Question

Prove that $\int_{X>\alpha}XdP\le\alpha(-\log F(\alpha))+\int_\alpha^\infty(-\log F(t))\lambda(dt)$

Proving a set has Lebesgue measure zero

Relating an integral over a sphere to an integral of a sphere one dimension smaller "without" using polar coordinates

Show $\int _{0} ^{\infty} \frac{|f(x)|}{|x-a|^b} dx <\infty$ for a.e. $a\in \mathbb{R}$ if $f$ Lebesgue integrable on $\mathbb{R}$, $b\in (0,1)$

Using polar coordinates with radial functions in two variables

An application of Lusin's theorem.

Help in trying to understand a proof : Lebesgue outer measure as infimum of a Lebesgue Measure.

Measure of self-sums of a particular meager set of measure zero.

Proving Lebesgue integrability of a bounded function

Writing an integral over a sphere in terms of integrals of another spheres with lower dimension

Is it always true that $\int_{\Omega_n} f h\ dx = 0$ for any $h \in C_c (\Omega_n)$ eventually?

Which is better to use $A\leq B$ or $A=B$ in a proof of a proposition?

Equimeasurable functions of $p(\cdot) :[0;1] \to [1;\infty)$ and $p(\cdot\cdot) : [0;1]^2 \to [1; \infty)$.

Proper notation for integration on manifolds?

Distribution of a dense subset in an interval

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