Question

If $f\in L^{1}((0,1))$, does it hold that $\lim\limits_{n\to+\infty}\int_{0}^{\frac{1}{n}}f(x)\mathrm{d}x=0$?

score 88 · Answer 1 · 2026-03-24 22:07:38

88

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If $f\in L^{1}((0,1))$, does it hold that $\lim\limits_{n\to+\infty}\int_{0}^{\frac{1}{n}}f(x)\mathrm{d}x=0$?

Published on 24 Mar 2026 - 22:07

score 1.1k · Answer 2 · 2026-04-09 00:27:09

1.1k

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How can a martingale be a density process?

Published on 09 Apr 2026 - 0:27

score 2.4k · Answer 3 · 2026-04-01 18:14:30

2.4k

Views

Kullback-Leibler divergence is equivalent to L2 norm in some cases?

Published on 01 Apr 2026 - 18:14

score 37 · Answer 4 · 2026-03-25 01:38:02

37

Views

If $g \in \mathcal{Re}(\lambda f)$, then $|\int fd\mu| = \int gd\mu $ and $i\int \mathcal{Im}(\lambda f)d\mu = 0$

Published on 25 Mar 2026 - 1:38

score 503 · Answer 5 · 2018-02-04 14:31:25

503

Views

Prove L1 convergence

Published on 04 Feb 2018 - 14:31

score 355 · Answer 6 · 2026-04-11 22:22:27

355

Views

Prove continuity of a function defined as a Lebesgue integral

Published on 11 Apr 2026 - 22:22

score 150 · Answer 7 · 2026-04-10 13:36:21

150

Views

How to derive the differential notation of Ito process

Published on 10 Apr 2026 - 13:36

score 101 · Answer 8 · 2018-02-04 20:49:18

101

Views

Calculate $\lim_{n\rightarrow +\infty}n\int_X\log\biggl(1+\frac{f(x)}{n}\biggl)d\mu$

Published on 04 Feb 2018 - 20:49

score 81 · Answer 9 · 2018-02-04 22:33:43

If $\mu$ is a vector measure and $\nu$ is a measure with $\left\|\mu\right\|\le\nu$ on a generating semiring, are we able to conclude $|\mu|\le\nu$?

score 217 · Answer 10 · 2018-02-05 01:10:56

Is there a Lebesgue integrable function $f$ such that the set of points on no neighborhood of which $f$ is bounded has positive Lebesgue measure?

score 98 · Answer 11 · 2026-04-09 02:08:37

98

Views

What type of measure is this?

Published on 09 Apr 2026 - 2:08

score 1.7k · Answer 12 · 2026-03-25 01:34:03

1.7k

Views

Lebesgue integrable implies Riemann integrable?

Published on 25 Mar 2026 - 1:34

score 145 · Answer 13 · 2026-04-11 03:57:13

145

Views

Estimating the measure of a sum of subsets

Published on 11 Apr 2026 - 3:57

score 151 · Answer 14 · 2018-02-05 14:54:49

151

Views

Different versions of Egoroff's theorem

Published on 05 Feb 2018 - 14:54

score 45 · Answer 15 · 2026-04-11 00:39:11

45

Views

Characteristic property of the total variation of a vector measure

Published on 11 Apr 2026 - 0:39

List Question

If $f\in L^{1}((0,1))$, does it hold that $\lim\limits_{n\to+\infty}\int_{0}^{\frac{1}{n}}f(x)\mathrm{d}x=0$?

How can a martingale be a density process?

Kullback-Leibler divergence is equivalent to L2 norm in some cases?

If $g \in \mathcal{Re}(\lambda f)$, then $|\int fd\mu| = \int gd\mu $ and $i\int \mathcal{Im}(\lambda f)d\mu = 0$

Prove L1 convergence

Prove continuity of a function defined as a Lebesgue integral

How to derive the differential notation of Ito process

Calculate $\lim_{n\rightarrow +\infty}n\int_X\log\biggl(1+\frac{f(x)}{n}\biggl)d\mu$

If $\mu$ is a vector measure and $\nu$ is a measure with $\left\|\mu\right\|\le\nu$ on a generating semiring, are we able to conclude $|\mu|\le\nu$?

Is there a Lebesgue integrable function $f$ such that the set of points on no neighborhood of which $f$ is bounded has positive Lebesgue measure?

What type of measure is this?

Lebesgue integrable implies Riemann integrable?

Estimating the measure of a sum of subsets

Different versions of Egoroff's theorem

Characteristic property of the total variation of a vector measure

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