Question

Confusion on Folland's redefinition of L^1 space.

score 89 · Answer 1 · 2024-02-17 23:48:55

89

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Confusion on Folland's redefinition of L^1 space.

Published on 17 Feb 2024 - 23:48

score 36 · Answer 2 · 2026-03-26 01:25:13

36

Views

For $f \in H^s$, then $\exists g \in C_c$ such that $f=g$ a.e.

Published on 26 Mar 2026 - 1:25

score 33 · Answer 3 · 2026-04-05 21:30:16

33

Views

Laplace Transform of a Piece-wise function with a Weibull distribution.

Published on 05 Apr 2026 - 21:30

score 132 · Answer 4 · 2026-04-12 11:25:30

132

Views

Defining the expectation of a measurable function with respect to a (non-probability) measure

Published on 12 Apr 2026 - 11:25

score 59 · Answer 5 · 2024-02-20 07:41:48

59

Views

Question concerning the correctness of this version of Fatou's Lemma

Published on 20 Feb 2024 - 7:41

score 116 · Answer 6 · 2026-04-13 14:36:09

116

Views

Approximating norm of a Hilbert space point with the norm of a vector

Published on 13 Apr 2026 - 14:36

score 113 · Answer 7 · 2026-04-14 04:06:51

113

Views

Define multiplication on $L^1(\mathbb{R})$

Published on 14 Apr 2026 - 4:06

score 54 · Answer 8 · 2024-02-22 23:44:28

54

Views

Does there exist a subset $S$ in $[0,1]$ such that for all interval, $S$ and its complement in the interval has the same Lebesgue masure?

Published on 22 Feb 2024 - 23:44

score 31 · Answer 9 · 2024-02-24 12:02:51

31

Views

Lebesgue integral and limit; $\lim_{a\to 0^+}\int_{a}^{1}(t\ln(t))^3dt=\int_{0}^{1}(t\ln(t))^3dt$

Published on 24 Feb 2024 - 12:02

score 30 · Answer 10 · 2026-04-13 08:55:09

30

Views

Subsequence which converges for compact metric space.

Published on 13 Apr 2026 - 8:55

score 104 · Answer 11 · 2026-04-13 09:35:19

104

Views

Example of a function on $([0,1]; \sigma ([0;1]); \lambda )$ for which it has no meaning to write $ \int f d \lambda$

Published on 13 Apr 2026 - 9:35

score 33 · Answer 12 · 2026-04-13 02:27:01

33

Views

Proving a given metric is a metric on the product of a measure space with itself.

Published on 13 Apr 2026 - 2:27

score 77 · Answer 13 · 2026-03-27 18:27:55

77

Views

Prove that $\int f \ln(f) d \mu =\sup \left \{ \int f \phi d \mu : \int e^{\phi} d\mu \leq 1 \right \}$

Published on 27 Mar 2026 - 18:27

score 65 · Answer 14 · 2026-04-12 19:27:11

65

Views

Finding a Lebesgue integrable function for every $1 \leqslant q < \infty$ that satisfies aditional requirement.

Published on 12 Apr 2026 - 19:27

score 26 · Answer 15 · 2026-04-11 21:53:46

26

Views

Convergence on $L^1$ space

Published on 11 Apr 2026 - 21:53

List Question

Confusion on Folland's redefinition of L^1 space.

For $f \in H^s$, then $\exists g \in C_c$ such that $f=g$ a.e.

Laplace Transform of a Piece-wise function with a Weibull distribution.

Defining the expectation of a measurable function with respect to a (non-probability) measure

Question concerning the correctness of this version of Fatou's Lemma

Approximating norm of a Hilbert space point with the norm of a vector

Define multiplication on $L^1(\mathbb{R})$

Does there exist a subset $S$ in $[0,1]$ such that for all interval, $S$ and its complement in the interval has the same Lebesgue masure?

Lebesgue integral and limit; $\lim_{a\to 0^+}\int_{a}^{1}(t\ln(t))^3dt=\int_{0}^{1}(t\ln(t))^3dt$

Subsequence which converges for compact metric space.

Example of a function on $([0,1]; \sigma ([0;1]); \lambda )$ for which it has no meaning to write $ \int f d \lambda$

Proving a given metric is a metric on the product of a measure space with itself.

Prove that $\int f \ln(f) d \mu =\sup \left \{ \int f \phi d \mu : \int e^{\phi} d\mu \leq 1 \right \}$

Finding a Lebesgue integrable function for every $1 \leqslant q < \infty$ that satisfies aditional requirement.

Convergence on $L^1$ space

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