Question

$f'(t)$ where $f(t)$ is not differentiable everywhere

score 72 · Answer 1 · 2018-04-19 12:02:22

72

Views

$f'(t)$ where $f(t)$ is not differentiable everywhere

Published on 19 Apr 2018 - 12:02

score 157 · Answer 2 · 2018-04-19 12:22:50

157

Views

Comparing $\lim_{n\to\infty}\int_{[0,1]}\frac{nx}{1+nx^2}$ and $\lim_{n\to\infty}\int_0^1 \frac{nx}{1+nx^2}dx$

Published on 19 Apr 2018 - 12:22

score 1.6k · Answer 3 · 2018-04-20 08:20:20

1.6k

Views

Product of two Lebesgue measurable set is measurable

Published on 20 Apr 2018 - 8:20

score 44 · Answer 4 · 2018-04-20 11:55:41

44

Views

If $h: E \rightarrow [0,\infty]$, and $\nu(A) = \int_{A}hd\mu$, then if $A \in \mathcal{A} $ such that $\mu(A) =0 $, we have $\nu (A) =0$

Published on 20 Apr 2018 - 11:55

score 76 · Answer 5 · 2026-03-25 13:57:03

76

Views

If $\|f\|_3 = \|g\|_3 = \int_E f^2 g =1,$ prove that $g(x) = |f(x)|$ for almost all $x \in E.$

Published on 25 Mar 2026 - 13:57

score 195 · Answer 6 · 2018-04-21 22:55:03

195

Views

Verifying integrability of $I = \int_{0}^{2}dx\int_{0}^{4-x^{2}}\left(\frac{xe^{2y}}{4-y}\right)dy$

Published on 21 Apr 2018 - 22:55

score 1.2k · Answer 7 · 2018-04-22 06:53:06

1.2k

Views

Proof check: continuous function with compact support is $\lambda^d$ integrable

Published on 22 Apr 2018 - 6:53

score 160 · Answer 8 · 2018-04-22 14:35:27

160

Views

Show that $\int_\Omega(\sum_{n=1}^{\infty}f_n)d\mu = \sum_{n=1}^{\infty}\int_\Omega f_nd\mu$ without monotone convergence

Published on 22 Apr 2018 - 14:35

score 152 · Answer 9 · 2026-03-22 18:53:28

152

Views

Question in Proof of Riesz Representation Theorem

Published on 22 Mar 2026 - 18:53

score 67 · Answer 10 · 2018-04-23 13:04:19

67

Views

Determine whether the following Lebesgue integral exists.

Published on 23 Apr 2018 - 13:04

score 50 · Answer 11 · 2018-04-23 17:22:46

50

Views

Why does this hold for all continuous functions?

Published on 23 Apr 2018 - 17:22

score 62 · Answer 12 · 2026-03-25 06:04:05

62

Views

On a bound for the application of the dominated convergence theorem.

Published on 25 Mar 2026 - 6:04

score 54 · Answer 13 · 2018-04-24 10:26:46

54

Views

A question on a proof that $ L^1 (E)$ is Complete

Published on 24 Apr 2018 - 10:26

score 186 · Answer 14 · 2026-03-22 06:27:47

186

Views

Bounded Variation Proof

Published on 22 Mar 2026 - 6:27

score 239 · Answer 15 · 2018-04-24 15:43:55

239

Views

Find the $L^1$ norm of the Dirichlet Function

Published on 24 Apr 2018 - 15:43

List Question

$f'(t)$ where $f(t)$ is not differentiable everywhere

Comparing $\lim_{n\to\infty}\int_{[0,1]}\frac{nx}{1+nx^2}$ and $\lim_{n\to\infty}\int_0^1 \frac{nx}{1+nx^2}dx$

Product of two Lebesgue measurable set is measurable

If $h: E \rightarrow [0,\infty]$, and $\nu(A) = \int_{A}hd\mu$, then if $A \in \mathcal{A} $ such that $\mu(A) =0 $, we have $\nu (A) =0$

If $\|f\|_3 = \|g\|_3 = \int_E f^2 g =1,$ prove that $g(x) = |f(x)|$ for almost all $x \in E.$

Verifying integrability of $I = \int_{0}^{2}dx\int_{0}^{4-x^{2}}\left(\frac{xe^{2y}}{4-y}\right)dy$

Proof check: continuous function with compact support is $\lambda^d$ integrable

Show that $\int_\Omega(\sum_{n=1}^{\infty}f_n)d\mu = \sum_{n=1}^{\infty}\int_\Omega f_nd\mu$ without monotone convergence

Question in Proof of Riesz Representation Theorem

Determine whether the following Lebesgue integral exists.

Why does this hold for all continuous functions?

On a bound for the application of the dominated convergence theorem.

A question on a proof that $ L^1 (E)$ is Complete

Bounded Variation Proof

Find the $L^1$ norm of the Dirichlet Function

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