Question

For which values of the parameter $\alpha$ function $f(x) = \frac{1}{x^{\alpha}}\left|sin\frac{1}{x}\right|$ is Lebesgue Integrable?

score 283 · Answer 1 · 2020-05-08 08:30:30

283

Views

For which values of the parameter $\alpha$ function $f(x) = \frac{1}{x^{\alpha}}\left|sin\frac{1}{x}\right|$ is Lebesgue Integrable?

Published on 08 May 2020 - 8:30

score 22 · Answer 2 · 2020-05-08 20:33:19

22

Views

Let $[0,1]=\cup A_n$ and assume that $\lambda(A_i\cap E_j) \to 0$ as $j\to \infty$ for all $i$. Show that $\lambda(E_j)\to 0$ ($E_j\subseteq [0,1]$)

Published on 08 May 2020 - 20:33

score 59 · Answer 3 · 2020-05-08 23:36:48

59

Views

Calculate $\lim\limits_{n \to \infty}\int\limits_{0}^{1} \frac{f_n(x)}{\sqrt{|x-\frac{1}{n}|}}$ given that $|f_n(x)|\leq 1$ and $f_n \to f$ pointwise.

Published on 08 May 2020 - 23:36

score 24 · Answer 4 · 2020-05-09 04:19:01

24

Views

Assume that $\lambda(A+t-A)=0$ for all $t \in Q$ show that either $A$ is a null set, or full measure.

Published on 09 May 2020 - 4:19

score 228 · Answer 5 · 2020-05-09 06:11:10

228

Views

Converge pointwise a.e. but not converge uniformly a.e.?

Published on 09 May 2020 - 6:11

score 53 · Answer 6 · 2020-05-09 09:24:01

53

Views

$\lim_{n\to \infty} \int_n^{n+1}f(x)~dx=0$ if $f\in L^2(\Bbb R)$

Published on 09 May 2020 - 9:24

score 395 · Answer 7 · 2020-05-09 15:01:57

395

Views

show that $cf$ is Lebesgue integrable

Published on 09 May 2020 - 15:01

score 121 · Answer 8 · 2020-05-09 15:24:12

121

Views

Prove $f(x)=\sum_{n=1}^\infty\frac{(-1)^n}{n}\chi_{[n-1,n)}(x)$ is not Lebesgue Integrable

Published on 09 May 2020 - 15:24

score 87 · Answer 9 · 2020-05-09 19:32:29

87

Views

Assume that $\|f\|_p\leq C$ for all $p\geq1$ show that $f \in L^\infty [0,1]$ [proof verificatoin]

Published on 09 May 2020 - 19:32

score 94 · Answer 10 · 2020-05-10 00:43:20

94

Views

Integration inequality $\int_0^1 fg\,dx \leq \int_0^1f\,dx\int_0^1g\,dx$

Published on 10 May 2020 - 0:43

score 121 · Answer 11 · 2020-05-10 07:39:10

121

Views

Property of Lebesgue integrable function proof verification

Published on 10 May 2020 - 7:39

score 1.1k · Answer 12 · 2020-05-11 18:18:16

1.1k

Views

Translation invariance of Lebesgue integral

Published on 11 May 2020 - 18:18

score 57 · Answer 13 · 2020-05-11 21:10:57

57

Views

I have a question on Lebesgue Integral Properties

Published on 11 May 2020 - 21:10

score 287 · Answer 14 · 2020-05-12 04:36:20

287

Views

Absolute value of integral equal to integral of absolute value

Published on 12 May 2020 - 4:36

score 145 · Answer 15 · 2020-05-12 09:09:22

145

Views

Clarification: Definition of moment / expected value - Measure Theory

Published on 12 May 2020 - 9:09

List Question

For which values of the parameter $\alpha$ function $f(x) = \frac{1}{x^{\alpha}}\left|sin\frac{1}{x}\right|$ is Lebesgue Integrable?

Let $[0,1]=\cup A_n$ and assume that $\lambda(A_i\cap E_j) \to 0$ as $j\to \infty$ for all $i$. Show that $\lambda(E_j)\to 0$ ($E_j\subseteq [0,1]$)

Calculate $\lim\limits_{n \to \infty}\int\limits_{0}^{1} \frac{f_n(x)}{\sqrt{|x-\frac{1}{n}|}}$ given that $|f_n(x)|\leq 1$ and $f_n \to f$ pointwise.

Assume that $\lambda(A+t-A)=0$ for all $t \in Q$ show that either $A$ is a null set, or full measure.

Converge pointwise a.e. but not converge uniformly a.e.?

$\lim_{n\to \infty} \int_n^{n+1}f(x)~dx=0$ if $f\in L^2(\Bbb R)$

show that $cf$ is Lebesgue integrable

Prove $f(x)=\sum_{n=1}^\infty\frac{(-1)^n}{n}\chi_{[n-1,n)}(x)$ is not Lebesgue Integrable

Assume that $\|f\|_p\leq C$ for all $p\geq1$ show that $f \in L^\infty [0,1]$ [proof verificatoin]

Integration inequality $\int_0^1 fg\,dx \leq \int_0^1f\,dx\int_0^1g\,dx$

Property of Lebesgue integrable function proof verification

Translation invariance of Lebesgue integral

I have a question on Lebesgue Integral Properties

Absolute value of integral equal to integral of absolute value

Clarification: Definition of moment / expected value - Measure Theory

Trending Questions

Popular # Hahtags

Popular Questions