Question

Determine which $p \in (0,\infty)$ where $f \in \mathcal{L}^p(\lambda)$.

score 57 · Answer 1 · 2026-03-29 04:48:11

57

Views

Determine which $p \in (0,\infty)$ where $f \in \mathcal{L}^p(\lambda)$.

Published on 29 Mar 2026 - 4:48

score 131 · Answer 2 · 2019-10-30 14:29:50

131

Views

Does the integral of a product of simple functions define an entire function?

Published on 30 Oct 2019 - 14:29

score 55 · Answer 3 · 2019-10-31 05:28:18

55

Views

If $f \in L^2(\mathbb{B})$ then $|x|^{-1} f(x) \in L^1(\mathbb{B})$

Published on 31 Oct 2019 - 5:28

score 1.3k · Answer 4 · 2019-10-31 06:31:24

1.3k

Views

Prove: If $f \in L^p(\mathbb{R}^n)$, then $f$ is locally integrable.

Published on 31 Oct 2019 - 6:31

score 43 · Answer 5 · 2026-02-24 00:46:46

43

Views

Convergence in $L^{2}$ of continuous nonnegative function to zero

Published on 24 Feb 2026 - 0:46

score 123 · Answer 6 · 2026-04-02 03:48:34

123

Views

Proving that the Lebesgue space $L^1$ is complete using absolute convergence of series

Published on 02 Apr 2026 - 3:48

score 126 · Answer 7 · 2019-10-31 22:35:07

126

Views

Why is the function $f(x) = \sin(2\pi x)$ not Lebesgue Integrable over $E$ such that $E = [1, \infty)$

Published on 31 Oct 2019 - 22:35

score 67 · Answer 8 · 2019-11-01 11:43:57

67

Views

$\sum_{k=1}^{\infty}|a_kb_k| < \infty$ $\forall \sum_{k=1}^\infty|a_k|$ convergent. Prove $\{b_k\}_{k=1}^\infty$ is bounded. For continuous functions?

Published on 01 Nov 2019 - 11:43

score 516 · Answer 9 · 2019-11-01 14:00:50

516

Views

Using Dominated Convergence Theorem when the bound is only for the limit

Published on 01 Nov 2019 - 14:00

score 405 · Answer 10 · 2019-11-01 19:34:50

405

Views

If integral is 0 on any set of measure 1/pi, then the function is 0 a.e.

Published on 01 Nov 2019 - 19:34

score 29 · Answer 11 · 2019-11-02 10:09:53

29

Views

Calculate $\sum_{n=0}^\infty \frac{1}{n!} \int_{[0,1]} x^n \frac{1}{e^{2x}} \, d\lambda(x)$

Published on 02 Nov 2019 - 10:09

score 43 · Answer 12 · 2019-11-02 13:13:53

$f:\mathbb{R} \rightarrow[0,\infty) $ is a measurable function, if $\int_{-\infty}^{\infty} f(x)=1$, then $\int_{-\infty}^0\frac{1}{1+f(x)}=\infty$

score 276 · Answer 13 · 2019-11-02 14:17:27

276

Views

How to make an infinite dimensional vector space complete?

Published on 02 Nov 2019 - 14:17

score 184 · Answer 14 · 2019-11-02 18:15:39

184

Views

Equality in Lebesgue measure theory

Published on 02 Nov 2019 - 18:15

score 79 · Answer 15 · 2026-03-26 17:36:05

79

Views

Weird mistake that I cannot spot in a proof

Published on 26 Mar 2026 - 17:36

List Question

Determine which $p \in (0,\infty)$ where $f \in \mathcal{L}^p(\lambda)$.

Does the integral of a product of simple functions define an entire function?

If $f \in L^2(\mathbb{B})$ then $|x|^{-1} f(x) \in L^1(\mathbb{B})$

Prove: If $f \in L^p(\mathbb{R}^n)$, then $f$ is locally integrable.

Convergence in $L^{2}$ of continuous nonnegative function to zero

Proving that the Lebesgue space $L^1$ is complete using absolute convergence of series

Why is the function $f(x) = \sin(2\pi x)$ not Lebesgue Integrable over $E$ such that $E = [1, \infty)$

$\sum_{k=1}^{\infty}|a_kb_k| < \infty$ $\forall \sum_{k=1}^\infty|a_k|$ convergent. Prove $\{b_k\}_{k=1}^\infty$ is bounded. For continuous functions?

Using Dominated Convergence Theorem when the bound is only for the limit

If integral is 0 on any set of measure 1/pi, then the function is 0 a.e.

Calculate $\sum_{n=0}^\infty \frac{1}{n!} \int_{[0,1]} x^n \frac{1}{e^{2x}} \, d\lambda(x)$

$f:\mathbb{R} \rightarrow[0,\infty) $ is a measurable function, if $\int_{-\infty}^{\infty} f(x)=1$, then $\int_{-\infty}^0\frac{1}{1+f(x)}=\infty$

How to make an infinite dimensional vector space complete?

Equality in Lebesgue measure theory

Weird mistake that I cannot spot in a proof

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