Question

Does the convergence to 0 in $L^2(0,T;L^2(B))$ where $|\mathbb{R}^{d}-B|<\infty$ imply the convergence in $L^2(0,T;L^2(\mathbb{R}^{d}))$?

score 87 · Answer 1 · 2020-07-11 00:49:29

Does the convergence to 0 in $L^2(0,T;L^2(B))$ where $|\mathbb{R}^{d}-B|<\infty$ imply the convergence in $L^2(0,T;L^2(\mathbb{R}^{d}))$?

score 549 · Answer 2 · 2020-07-12 17:22:09

549

Views

Limit of sequence of Lebesgue integrable functions is not Lebesgue integrable

Published on 12 Jul 2020 - 17:22

score 121 · Answer 3 · 2020-07-12 19:32:48

121

Views

Criterion of Lebesgue integrability of finite measurable function

Published on 12 Jul 2020 - 19:32

score 31 · Answer 4 · 2026-03-25 17:38:59

31

Views

Show that there exists a unique measure $\pi$ on $\mathcal{B}[0,\infty)\otimes\mathcal{P}(\mathbb{N})$

Published on 25 Mar 2026 - 17:38

score 210 · Answer 5 · 2020-07-14 14:19:23

210

Views

Proof inner-product on square-integrable products is always well defined?

Published on 14 Jul 2020 - 14:19

score 42 · Answer 6 · 2026-03-25 23:42:26

42

Views

Bounds on Integral $\int_{0}^{t}\sin(2\pi\omega \tau)d\eta(\tau)$, where the function $\eta(\tau)$ is of bounded variation

Published on 25 Mar 2026 - 23:42

score 32 · Answer 7 · 2020-07-17 05:05:35

32

Views

Well-definedness of $\mu$-integral

Published on 17 Jul 2020 - 5:05

score 55 · Answer 8 · 2026-03-25 19:10:25

55

Views

A question of why these integrands can be taken out of the integrals.

Published on 25 Mar 2026 - 19:10

score 104 · Answer 9 · 2020-07-19 20:04:05

104

Views

What is the importance of the measure space $(\Omega,\mathcal{F},\mu)$ and the measurability of $f$ in the definition of integral?

Published on 19 Jul 2020 - 20:04

score 329 · Answer 10 · 2020-07-20 00:22:09

329

Views

If Lebesgue integral of nonnegative measurable function on $[0,x]$ is one-to-one, is $f$ positive almost everywhere?

Published on 20 Jul 2020 - 0:22

score 336 · Answer 11 · 2020-07-20 09:56:06

336

Views

A function finite almost everywhere but NOT Lebesgue integrable

Published on 20 Jul 2020 - 9:56

score 58 · Answer 12 · 2026-03-26 02:53:49

58

Views

Example of Non-Linear but Continuous Functionals on Bochner Space

Published on 26 Mar 2026 - 2:53

score 277 · Answer 13 · 2026-03-29 11:44:36

277

Views

How do we calculate the integral of measurable functions which are not Riemann integrable?

Published on 29 Mar 2026 - 11:44

score 64 · Answer 14 · 2020-07-22 04:45:21

64

Views

Evaluating $\lim_{n\rightarrow\infty}\int_0^n\frac{(1-\frac{x}{n})^n}{ne^{-x}}dx$

Published on 22 Jul 2020 - 4:45

score 38 · Answer 15 · 2020-07-22 07:22:11

38

Views

Question about dominated convergence: showing $1_{[\tau, \tau_j)}$ tends to $0$ a.e. for an approximating sequence of stopping times $\tau_j$.

Published on 22 Jul 2020 - 7:22

List Question

Does the convergence to 0 in $L^2(0,T;L^2(B))$ where $|\mathbb{R}^{d}-B|<\infty$ imply the convergence in $L^2(0,T;L^2(\mathbb{R}^{d}))$?

Limit of sequence of Lebesgue integrable functions is not Lebesgue integrable

Criterion of Lebesgue integrability of finite measurable function

Show that there exists a unique measure $\pi$ on $\mathcal{B}[0,\infty)\otimes\mathcal{P}(\mathbb{N})$

Proof inner-product on square-integrable products is always well defined?

Bounds on Integral $\int_{0}^{t}\sin(2\pi\omega \tau)d\eta(\tau)$, where the function $\eta(\tau)$ is of bounded variation

Well-definedness of $\mu$-integral

A question of why these integrands can be taken out of the integrals.

What is the importance of the measure space $(\Omega,\mathcal{F},\mu)$ and the measurability of $f$ in the definition of integral?

If Lebesgue integral of nonnegative measurable function on $[0,x]$ is one-to-one, is $f$ positive almost everywhere?

A function finite almost everywhere but NOT Lebesgue integrable

Example of Non-Linear but Continuous Functionals on Bochner Space

How do we calculate the integral of measurable functions which are not Riemann integrable?

Evaluating $\lim_{n\rightarrow\infty}\int_0^n\frac{(1-\frac{x}{n})^n}{ne^{-x}}dx$

Question about dominated convergence: showing $1_{[\tau, \tau_j)}$ tends to $0$ a.e. for an approximating sequence of stopping times $\tau_j$.

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