Question

If $0 < p < 1$, then $\int_X \log|f| \,d\mu \le \log \|f\|_p$ using Jensen's inequality

score 33 · Answer 1 · 2026-04-17 01:01:49

33

Views

If $0 < p < 1$, then $\int_X \log|f| \,d\mu \le \log \|f\|_p$ using Jensen's inequality

Published on 17 Apr 2026 - 1:01

score 55 · Answer 2 · 2026-04-15 18:51:43

55

Views

If $\lambda(f_n^{-1}(U))$ converges for all measurable sets $U,$ does $\{f_n\}$ have a convergent subsequence?

Published on 15 Apr 2026 - 18:51

score 65 · Answer 3 · 2026-03-25 17:26:55

65

Views

If $f,g$ are two measurable functions on $[0,1]$ such that $\int_A f=\int_A g$ for all $A\subset[0,1]$ such that $\mu(A)=1/3$. Then $f=g$ a.e. $\mu$

Published on 25 Mar 2026 - 17:26

score 52 · Answer 4 · 2026-04-12 17:48:25

52

Views

Calculating a limit of a sequence of integrals

Published on 12 Apr 2026 - 17:48

score 41 · Answer 5 · 2026-04-09 16:31:30

41

Views

Question about a notation in measure theory

Published on 09 Apr 2026 - 16:31

score 35 · Answer 6 · 2026-04-15 18:00:16

35

Views

If $\lambda(f_n^{-1}(A) \cap g_n^{-1}(B))$ converges for all measurable sets $A, B,$ do $f_n, g_n$ converge under $\lambda$?

Published on 15 Apr 2026 - 18:00

score 98 · Answer 7 · 2026-04-11 08:53:23

98

Views

Good family of approximations to the identity

Published on 11 Apr 2026 - 8:53

score 90 · Answer 8 · 2026-04-14 03:37:52

90

Views

If $A, B$ is a non-trivial partition of $S^1$, is it possible that $R_\theta(A) \cap B$ has measure zero for all rotations $R_\theta$?

Published on 14 Apr 2026 - 3:37

score 76 · Answer 9 · 2026-03-25 23:08:06

76

Views

Showing that a function is nonnegative almost everywhere on (0,1)

Published on 25 Mar 2026 - 23:08

score 54 · Answer 10 · 2026-04-15 12:47:02

54

Views

How does one find the expected value of the Conway base-13 function $f:\mathbb{R}\to\mathbb{R}$, when restricted to $f:[0,1]\to[0,1]$?

Published on 15 Apr 2026 - 12:47

score 30 · Answer 11 · 2026-04-11 22:12:15

30

Views

Understanding notation regarding the convolution of Dirac measures.

Published on 11 Apr 2026 - 22:12

score 37 · Answer 12 · 2026-04-10 23:51:13

37

Views

What is the Lebesgue measure of points that are close to a rational?

Published on 10 Apr 2026 - 23:51

score 124 · Answer 13 · 2026-04-17 15:56:20

124

Views

Convergence a.e. of $\sum_{n=1}^{\infty} \frac{a_n}{\sqrt{\left|x-r_n\right|}}$, where $\sum_{n=1}^{\infty}\left|a_n\right|<\infty$

Published on 17 Apr 2026 - 15:56

score 73 · Answer 14 · 2026-04-15 10:21:30

73

Views

Is there a Quick Way of Proving this Particular Case of the Lebesgue Differentiation Theorem?

Published on 15 Apr 2026 - 10:21

score 61 · Answer 15 · 2026-04-12 07:50:22

61

Views

Dual norm of integral vector norm

Published on 12 Apr 2026 - 7:50

List Question

If $0 < p < 1$, then $\int_X \log|f| \,d\mu \le \log \|f\|_p$ using Jensen's inequality

If $\lambda(f_n^{-1}(U))$ converges for all measurable sets $U,$ does $\{f_n\}$ have a convergent subsequence?

If $f,g$ are two measurable functions on $[0,1]$ such that $\int_A f=\int_A g$ for all $A\subset[0,1]$ such that $\mu(A)=1/3$. Then $f=g$ a.e. $\mu$

Calculating a limit of a sequence of integrals

Question about a notation in measure theory

If $\lambda(f_n^{-1}(A) \cap g_n^{-1}(B))$ converges for all measurable sets $A, B,$ do $f_n, g_n$ converge under $\lambda$?

Good family of approximations to the identity

If $A, B$ is a non-trivial partition of $S^1$, is it possible that $R_\theta(A) \cap B$ has measure zero for all rotations $R_\theta$?

Showing that a function is nonnegative almost everywhere on (0,1)

How does one find the expected value of the Conway base-13 function $f:\mathbb{R}\to\mathbb{R}$, when restricted to $f:[0,1]\to[0,1]$?

Understanding notation regarding the convolution of Dirac measures.

What is the Lebesgue measure of points that are close to a rational?

Convergence a.e. of $\sum_{n=1}^{\infty} \frac{a_n}{\sqrt{\left|x-r_n\right|}}$, where $\sum_{n=1}^{\infty}\left|a_n\right|<\infty$

Is there a Quick Way of Proving this Particular Case of the Lebesgue Differentiation Theorem?

Dual norm of integral vector norm

Trending Questions

Popular # Hahtags

Popular Questions