Question

Proving the inequality $\int_X f\ln f d\mu-\int_X f d\mu\ln \int_X f d\mu\ge \int_X f\ln g d\mu-\int_X f d\mu\ln \int_X g d\mu$

score 130 · Answer 1 · 2026-03-25 00:04:24

130

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Proving the inequality $\int_X f\ln f d\mu-\int_X f d\mu\ln \int_X f d\mu\ge \int_X f\ln g d\mu-\int_X f d\mu\ln \int_X g d\mu$

Published on 25 Mar 2026 - 0:04

score 46 · Answer 2 · 2018-03-24 17:01:25

46

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Is it true that if $f\in L^p(\mu)$, then $|\int_n^{n+1} f(x)dx| \leq \int_n^{n+1} |f(x)|dx$?

Published on 24 Mar 2018 - 17:01

score 93 · Answer 3 · 2026-03-22 19:32:19

93

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Do we have an integration version of Weyl's inequality?

Published on 22 Mar 2026 - 19:32

score 405 · Answer 4 · 2018-03-27 19:53:15

405

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Integral inequality for harmonic functions: $\frac{\int_{|w|=1}u^2(Rw)dS(w)}{\int_{|w|=1}u^2(rw)dS(w)}\leq \left(\frac{R}{r}\right)^{2N(R)}$

Published on 27 Mar 2018 - 19:53

score 304 · Answer 5 · 2026-03-21 22:22:56

304

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Prove the integral inequality

Published on 21 Mar 2026 - 22:22

score 282 · Answer 6 · 2026-03-17 21:11:52

282

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Simple L^2 bound for bivariate Sobolev function on a square

Published on 17 Mar 2026 - 21:11

score 316 · Answer 7 · 2018-03-30 01:52:32

316

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Maximizing expectation integral given PDF inequality

Published on 30 Mar 2018 - 1:52

score 588 · Answer 8 · 2018-03-30 06:07:56

588

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How can we prove that $\pi > 3$ using this definition

Published on 30 Mar 2018 - 6:07

score 98 · Answer 9 · 2018-03-30 18:37:41

98

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Prove $\int_\pi^{2\pi}\frac{\left|\sin(nx)\right|}xdx\leq\frac2{\displaystyle\pi}(\frac1{n+1}+\frac1{n+2}+......+\frac1{2n})$

Published on 30 Mar 2018 - 18:37

score 138 · Answer 10 · 2026-03-22 17:12:10

138

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An elementary (interpolation) inequality?

Published on 22 Mar 2026 - 17:12

score 143 · Answer 11 · 2018-04-06 09:03:28

143

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$g$ is positive and continuous , $f$ is increasing and differentiable on $[0,1]$, $f(0)=1$. Prove that $g(x)\leq f(x), \forall x \in [0,1].$

Published on 06 Apr 2018 - 9:03

score 435 · Answer 12 · 2026-03-21 20:57:52

435

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Ratio of integrals

Published on 21 Mar 2026 - 20:57

score 605 · Answer 13 · 2018-04-09 13:10:48

605

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$f$ convex, $g$ concave and increasing, $\int_0^1 f = \int_0^1 g$, then $\int_0^1(f)^2 \geq \int_0^1(g)^2$

Published on 09 Apr 2018 - 13:10

score 1.5k · Answer 14 · 2018-04-13 18:37:00

1.5k

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Bound on $L^2$ norm of gradient using $L^2$ norm of function

Published on 13 Apr 2018 - 18:37

score 126 · Answer 15 · 2026-03-22 20:34:35

126

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Having trouble showing this inequality

Published on 22 Mar 2026 - 20:34

List Question

Proving the inequality $\int_X f\ln f d\mu-\int_X f d\mu\ln \int_X f d\mu\ge \int_X f\ln g d\mu-\int_X f d\mu\ln \int_X g d\mu$

Is it true that if $f\in L^p(\mu)$, then $|\int_n^{n+1} f(x)dx| \leq \int_n^{n+1} |f(x)|dx$?

Do we have an integration version of Weyl's inequality?

Integral inequality for harmonic functions: $\frac{\int_{|w|=1}u^2(Rw)dS(w)}{\int_{|w|=1}u^2(rw)dS(w)}\leq \left(\frac{R}{r}\right)^{2N(R)}$

Prove the integral inequality

Simple L^2 bound for bivariate Sobolev function on a square

Maximizing expectation integral given PDF inequality

How can we prove that $\pi > 3$ using this definition

Prove $\int_\pi^{2\pi}\frac{\left|\sin(nx)\right|}xdx\leq\frac2{\displaystyle\pi}(\frac1{n+1}+\frac1{n+2}+......+\frac1{2n})$

An elementary (interpolation) inequality?

$g$ is positive and continuous , $f$ is increasing and differentiable on $[0,1]$, $f(0)=1$. Prove that $g(x)\leq f(x), \forall x \in [0,1].$

Ratio of integrals

$f$ convex, $g$ concave and increasing, $\int_0^1 f = \int_0^1 g$, then $\int_0^1(f)^2 \geq \int_0^1(g)^2$

Bound on $L^2$ norm of gradient using $L^2$ norm of function

Having trouble showing this inequality

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