Question

Prove that $\int _0 ^\infty f(x)g(cx)dx \to Mg(0) (c\to0)$

score 145 · Answer 1 · 2018-04-06 12:58:36

145

Views

Prove that $\int _0 ^\infty f(x)g(cx)dx \to Mg(0) (c\to0)$

Published on 06 Apr 2018 - 12:58

score 467 · Answer 2 · 2018-04-06 14:38:57

467

Views

Can a function be well-defined on an integral of $\mathbb{R}$ but not Lebesgue integrable?

Published on 06 Apr 2018 - 14:38

score 177 · Answer 3 · 2018-04-07 11:02:09

177

Views

Prove $\lim_{r \to 0} \frac{1}{2r} \int_{x-r}^{x+r} f(z) dz = f(x)$

Published on 07 Apr 2018 - 11:02

score 139 · Answer 4 · 2018-04-07 11:22:12

139

Views

Lebesgue integration criteria - Verify integrability

Published on 07 Apr 2018 - 11:22

score 378 · Answer 5 · 2018-04-07 17:58:30

378

Views

Lebesgue integral of $x \to \cos(x)$

Published on 07 Apr 2018 - 17:58

score 952 · Answer 6 · 2018-04-07 22:13:51

952

Views

Lebesgue integral of the extended Cantor function

Published on 07 Apr 2018 - 22:13

score 654 · Answer 7 · 2018-04-08 01:23:57

654

Views

Lebesgue integral of a function that is measurable, finite almost everywhere, and integrable on a set of finite measure

Published on 08 Apr 2018 - 1:23

score 54 · Answer 8 · 2018-04-08 11:34:52

54

Views

Integral over product space with one singularity is finite

Published on 08 Apr 2018 - 11:34

score 312 · Answer 9 · 2018-04-09 00:34:02

312

Views

An counterexample for the monotone convergence theorem and dominated convergence theorem

Published on 09 Apr 2018 - 0:34

score 95 · Answer 10 · 2018-04-09 04:51:42

95

Views

When do integrals converge, but absolute values of integrals not converge?

Published on 09 Apr 2018 - 4:51

score 3.2k · Answer 11 · 2018-04-09 21:02:56

3.2k

Views

Why is $\sin(x)/x$ not Lebesgue integrable?

Published on 09 Apr 2018 - 21:02

score 76 · Answer 12 · 2026-03-19 23:45:40

76

Views

If $\lim_{k \rightarrow \infty} g_k(x)=g(x) \text{, and } \lim_{k \rightarrow \infty} g_k^{'}(x)=f(x) \text{ a.e.}$ show $g^{'}(x)=f(x) \text{ a.e.}$

Published on 19 Mar 2026 - 23:45

score 104 · Answer 13 · 2018-04-10 11:58:03

104

Views

How can I solve this sequence with Riemann integration?

Published on 10 Apr 2018 - 11:58

score 283 · Answer 14 · 2026-03-25 05:07:06

283

Views

Prove $\|A\| \leq \|A\|_{HS}$, where $\|A\|$ is the operator norm of A

Published on 25 Mar 2026 - 5:07

score 247 · Answer 15 · 2026-03-19 18:58:21

247

Views

Suppose $f(x)$ is of bounded variation. Show $F(x) = \frac{1}{x} \int_0^x f(t) \, dt$ is also of bounded variation.

Published on 19 Mar 2026 - 18:58

List Question

Prove that $\int _0 ^\infty f(x)g(cx)dx \to Mg(0) (c\to0)$

Can a function be well-defined on an integral of $\mathbb{R}$ but not Lebesgue integrable?

Prove $\lim_{r \to 0} \frac{1}{2r} \int_{x-r}^{x+r} f(z) dz = f(x)$

Lebesgue integration criteria - Verify integrability

Lebesgue integral of $x \to \cos(x)$

Lebesgue integral of the extended Cantor function

Lebesgue integral of a function that is measurable, finite almost everywhere, and integrable on a set of finite measure

Integral over product space with one singularity is finite

An counterexample for the monotone convergence theorem and dominated convergence theorem

When do integrals converge, but absolute values of integrals not converge?

Why is $\sin(x)/x$ not Lebesgue integrable?

If $\lim_{k \rightarrow \infty} g_k(x)=g(x) \text{, and } \lim_{k \rightarrow \infty} g_k^{'}(x)=f(x) \text{ a.e.}$ show $g^{'}(x)=f(x) \text{ a.e.}$

How can I solve this sequence with Riemann integration?

Prove $\|A\| \leq \|A\|_{HS}$, where $\|A\|$ is the operator norm of A

Suppose $f(x)$ is of bounded variation. Show $F(x) = \frac{1}{x} \int_0^x f(t) \, dt$ is also of bounded variation.

Trending Questions

Popular # Hahtags

Popular Questions