Question

Show that there exists a sequence of positive real numbers $C_{n}$ such that $sup_{n}\dfrac{|f_{n}(x)|}{C_{n}}<\epsilon$ for all $x\in X\setminus E $

score 89 · Answer 1 · 2020-07-04 14:47:46

Show that there exists a sequence of positive real numbers $C_{n}$ such that $sup_{n}\dfrac{|f_{n}(x)|}{C_{n}}<\epsilon$ for all $x\in X\setminus E $

score 68 · Answer 2 · 2026-03-25 13:05:10

68

Views

Continuous Functions with countably many jump discontinuitites

Published on 25 Mar 2026 - 13:05

score 440 · Answer 3 · 2020-07-06 17:32:10

440

Views

Beppo Levi's Monotone Convergence Theorem

Published on 06 Jul 2020 - 17:32

score 104 · Answer 4 · 2020-07-14 18:47:54

104

Views

Doubt in Dominated Convergence theorem

Published on 14 Jul 2020 - 18:47

score 265 · Answer 5 · 2026-02-23 11:49:07

265

Views

Solving the functional equation $f(x)f(y)=c\,f(\sqrt{x^{2}+y^{2}})$

Published on 23 Feb 2026 - 11:49

score 70 · Answer 6 · 2020-07-17 00:50:57

70

Views

How do we prove that $\sup_{n\geq 1}f_{n}$ is a measurable function when each term $f_{n}$ is measurable?

Published on 17 Jul 2020 - 0:50

score 94 · Answer 7 · 2020-07-18 01:06:47

94

Views

The integral of a nonnegative measurable function definition: what does $f_n(\omega)\uparrow f(\omega)$ mean?

Published on 18 Jul 2020 - 1:06

score 79 · Answer 8 · 2020-07-19 08:56:38

79

Views

Measurabilty of supremum

Published on 19 Jul 2020 - 8:56

score 43 · Answer 9 · 2026-03-25 13:56:58

43

Views

Choosing a "canonical" representant of a class of measurable functions based on the essential range

Published on 25 Mar 2026 - 13:56

score 122 · Answer 10 · 2026-03-25 11:32:39

122

Views

Let $f$ be measurable then prove a certain set is measurable.

Published on 25 Mar 2026 - 11:32

score 276 · Answer 11 · 2020-07-21 18:19:25

276

Views

How do we calculate the integral of measurable functions which are not Riemann integrable?

Published on 21 Jul 2020 - 18:19

score 57 · Answer 12 · 2020-07-22 17:14:25

57

Views

Showing that the integral $\omega \mapsto\int_{\tau_{n-1}}^{\tau_n} f(s,\omega)ds$ is $\mathscr{F}_{\tau_n}$ measurable for stopping times $\tau_n$

Published on 22 Jul 2020 - 17:14

score 160 · Answer 13 · 2020-07-22 19:24:18

160

Views

Does $\int_1^\infty\frac{f_ng_n}{f_n^2+g_n}dx$ go to $0$ under these conditions of $f_n$ and $g_n$

Published on 22 Jul 2020 - 19:24

score 35 · Answer 14 · 2020-07-23 00:52:58

35

Views

How to prove $\phi'(t)1_{\Omega_t}(w)$ is measurable?

Published on 23 Jul 2020 - 0:52

score 75 · Answer 15 · 2026-03-28 20:51:55

75

Views

I need help with Dudley problem 4.2.6

Published on 28 Mar 2026 - 20:51

List Question

Show that there exists a sequence of positive real numbers $C_{n}$ such that $sup_{n}\dfrac{|f_{n}(x)|}{C_{n}}<\epsilon$ for all $x\in X\setminus E $

Continuous Functions with countably many jump discontinuitites

Beppo Levi's Monotone Convergence Theorem

Doubt in Dominated Convergence theorem

Solving the functional equation $f(x)f(y)=c\,f(\sqrt{x^{2}+y^{2}})$

How do we prove that $\sup_{n\geq 1}f_{n}$ is a measurable function when each term $f_{n}$ is measurable?

The integral of a nonnegative measurable function definition: what does $f_n(\omega)\uparrow f(\omega)$ mean?

Measurabilty of supremum

Choosing a "canonical" representant of a class of measurable functions based on the essential range

Let $f$ be measurable then prove a certain set is measurable.

How do we calculate the integral of measurable functions which are not Riemann integrable?

Showing that the integral $\omega \mapsto\int_{\tau_{n-1}}^{\tau_n} f(s,\omega)ds$ is $\mathscr{F}_{\tau_n}$ measurable for stopping times $\tau_n$

Does $\int_1^\infty\frac{f_ng_n}{f_n^2+g_n}dx$ go to $0$ under these conditions of $f_n$ and $g_n$

How to prove $\phi'(t)1_{\Omega_t}(w)$ is measurable?

I need help with Dudley problem 4.2.6

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