Question

Show that if $\frac{1}{\mu\left(E\right)}\cdot\int_{E}fd\mu\in C$ for all $E$ with $\mu\left(E\right)>0$ then $f\left(x\right)\in C$ almost surely

score 169 · Answer 1 · 2026-04-14 16:55:46

169

Views

Show that if $\frac{1}{\mu\left(E\right)}\cdot\int_{E}fd\mu\in C$ for all $E$ with $\mu\left(E\right)>0$ then $f\left(x\right)\in C$ almost surely

Published on 14 Apr 2026 - 16:55

score 183 · Answer 2 · 2026-04-12 04:41:32

183

Views

proving inequality involving lebesgue measurable function on [0,1]

Published on 12 Apr 2026 - 4:41

score 331 · Answer 3 · 2026-04-11 22:50:42

331

Views

Solution to heat equation, differentiation under integral sign

Published on 11 Apr 2026 - 22:50

score 116 · Answer 4 · 2026-04-16 14:24:19

116

Views

Suppose $\mu(X)<\infty$. Show that if $\ f\in\ L^q(X,\mu)$ for some $1\le q<\infty$ then $\ f\in\ L^r(X,\mu)$ for $1\le r<q$

Published on 16 Apr 2026 - 14:24

score 153 · Answer 5 · 2026-04-17 11:24:14

153

Views

Which quantity is greater: $\int_{0}^{1} f(x)\log f(x)dx$ or $\int_{0}^{1} f(y)dy\int_{0}^{1} \log f(w)dw$?

Published on 17 Apr 2026 - 11:24

score 263 · Answer 6 · 2026-04-15 21:55:38

263

Views

If $f_n \rightarrow f$ a.e. on $A, \lambda(A) < \infty$ then $\lim_{n\rightarrow \infty} \int_A f_n(x) dx = \int_A f(x) dx$

Published on 15 Apr 2026 - 21:55

score 71 · Answer 7 · 2026-04-09 18:36:59

71

Views

Which integral is greater?

Published on 09 Apr 2026 - 18:36

score 53 · Answer 8 · 2026-04-13 01:35:12

53

Views

Show divergence in $L_1$

Published on 13 Apr 2026 - 1:35

score 251 · Answer 9 · 2026-04-12 18:59:30

251

Views

question 6.09 from Folland Real Analysis

Published on 12 Apr 2026 - 18:59

score 47 · Answer 10 · 2026-04-09 16:55:16

47

Views

density of spaces, Lebesgue

Published on 09 Apr 2026 - 16:55

score 546 · Answer 11 · 2026-04-11 09:50:54

546

Views

Theorem of Lebesgue and differentiation of a parameter integral

Published on 11 Apr 2026 - 9:50

score 1.2k · Answer 12 · 2026-04-24 02:23:24

1.2k

Views

Uniform convergence and convergence of integrals

Published on 24 Apr 2026 - 2:23

score 694 · Answer 13 · 2026-04-12 04:21:54

694

Views

Parameter integral and continuity (Theorem of Lebesgue)

Published on 12 Apr 2026 - 4:21

score 282 · Answer 14 · 2026-04-12 15:25:18

282

Views

Comparing two integrals

Published on 12 Apr 2026 - 15:25

score 93 · Answer 15 · 2026-04-29 01:01:42

93

Views

Is there a sequence $(f_n)\in\ L^2([0,1])$, s.t. $\lVert f_n\rVert_2=1$, $\forall n$, but it has no convergent subsequences in $L^2([0,1])$ ?

Published on 29 Apr 2026 - 1:01

List Question

Show that if $\frac{1}{\mu\left(E\right)}\cdot\int_{E}fd\mu\in C$ for all $E$ with $\mu\left(E\right)>0$ then $f\left(x\right)\in C$ almost surely

proving inequality involving lebesgue measurable function on [0,1]

Solution to heat equation, differentiation under integral sign

Suppose $\mu(X)<\infty$. Show that if $\ f\in\ L^q(X,\mu)$ for some $1\le q<\infty$ then $\ f\in\ L^r(X,\mu)$ for $1\le r<q$

Which quantity is greater: $\int_{0}^{1} f(x)\log f(x)dx$ or $\int_{0}^{1} f(y)dy\int_{0}^{1} \log f(w)dw$?

If $f_n \rightarrow f$ a.e. on $A, \lambda(A) < \infty$ then $\lim_{n\rightarrow \infty} \int_A f_n(x) dx = \int_A f(x) dx$

Which integral is greater?

Show divergence in $L_1$

question 6.09 from Folland Real Analysis

density of spaces, Lebesgue

Theorem of Lebesgue and differentiation of a parameter integral

Uniform convergence and convergence of integrals

Parameter integral and continuity (Theorem of Lebesgue)

Comparing two integrals

Is there a sequence $(f_n)\in\ L^2([0,1])$, s.t. $\lVert f_n\rVert_2=1$, $\forall n$, but it has no convergent subsequences in $L^2([0,1])$ ?

Trending Questions

Popular # Hahtags

Popular Questions