Question

Show that if $X$ is a bounded random variable, then its characteristic function is a power series with an infinite radius of convergence.

score 575 · Answer 1 · 2026-03-25 14:14:04

575

Views

Show that if $X$ is a bounded random variable, then its characteristic function is a power series with an infinite radius of convergence.

Published on 25 Mar 2026 - 14:14

score 57 · Answer 2 · 2026-04-16 17:09:45

57

Views

Counterexamples to $\{f_n\} \subseteq L^1(\mu)$, $f_n \to f$ uniformly, $\mu(X) = \infty$ then $f \in L^1(\mu)$

Published on 16 Apr 2026 - 17:09

score 136 · Answer 3 · 2026-04-13 17:47:32

136

Views

Show that a function is finite but unbounded in a algebra

Published on 13 Apr 2026 - 17:47

score 1.6k · Answer 4 · 2026-04-14 11:24:47

1.6k

Views

Why can Lebesgue integral be defined only with supremum, but Riemanns needs both sup. and inf.?

Published on 14 Apr 2026 - 11:24

score 115 · Answer 5 · 2026-04-16 01:56:34

115

Views

Showing convergence of joint random variables

Published on 16 Apr 2026 - 1:56

score 67 · Answer 6 · 2026-04-09 20:23:32

67

Views

The Limits of Measurable Functions

Published on 09 Apr 2026 - 20:23

score 134 · Answer 7 · 2026-04-16 13:01:57

134

Views

A kind of martingale convergence theorem

Published on 16 Apr 2026 - 13:01

score 187 · Answer 8 · 2026-04-14 16:52:21

187

Views

Applying Jensen's inequality to show $\sqrt[n]{y_1...y_n} \ \leq \frac{y_1+...+y_n}{n}$

Published on 14 Apr 2026 - 16:52

score 55 · Answer 9 · 2026-04-16 06:55:24

55

Views

If $A = \int_Xf\ d\mu$, then $\sqrt{1+A^2} \ \le \ \int_x\sqrt{x+f^2}\ d\mu \ \le \ 1+A $

Published on 16 Apr 2026 - 6:55

score 56 · Answer 10 · 2026-04-16 03:09:54

56

Views

How can we show that $\sigma(M_\phi) = \text{ess range} \phi$?

Published on 16 Apr 2026 - 3:09

score 683 · Answer 11 · 2026-03-25 03:07:50

683

Views

Geometric measure theory on manifolds: suggested book

Published on 25 Mar 2026 - 3:07

score 63 · Answer 12 · 2026-04-12 00:56:32

63

Views

Brownian Motion, Measurability of $C([0,\infty))$

Published on 12 Apr 2026 - 0:56

score 271 · Answer 13 · 2026-04-16 22:57:23

271

Views

Smallest $\sigma$-algebra containing $\mathcal{U}$ (Oksendal SDE exercise 2.18)

Published on 16 Apr 2026 - 22:57

score 216 · Answer 14 · 2026-04-13 02:10:55

216

Views

if $E \subset \mathbb R^n$ is compact, then $E$ is null-set

Published on 13 Apr 2026 - 2:10

score 112 · Answer 15 · 2026-04-16 22:55:52

112

Views

Showing $m^(A-E)=m^(A)$ when $m^*(E)=0$

Published on 16 Apr 2026 - 22:55

List Question

Show that if $X$ is a bounded random variable, then its characteristic function is a power series with an infinite radius of convergence.

Counterexamples to $\{f_n\} \subseteq L^1(\mu)$, $f_n \to f$ uniformly, $\mu(X) = \infty$ then $f \in L^1(\mu)$

Show that a function is finite but unbounded in a algebra

Why can Lebesgue integral be defined only with supremum, but Riemanns needs both sup. and inf.?

Showing convergence of joint random variables

The Limits of Measurable Functions

A kind of martingale convergence theorem

Applying Jensen's inequality to show $\sqrt[n]{y_1...y_n} \ \leq \frac{y_1+...+y_n}{n}$

If $A = \int_Xf\ d\mu$, then $\sqrt{1+A^2} \ \le \ \int_x\sqrt{x+f^2}\ d\mu \ \le \ 1+A $

How can we show that $\sigma(M_\phi) = \text{ess range} \phi$?

Geometric measure theory on manifolds: suggested book

Brownian Motion, Measurability of $C([0,\infty))$

Smallest $\sigma$-algebra containing $\mathcal{U}$ (Oksendal SDE exercise 2.18)

if $E \subset \mathbb R^n$ is compact, then $E$ is null-set

Showing $m^(A-E)=m^(A)$ when $m^*(E)=0$

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