Question

Pointwise convergence of $X_n$ vs $X_nI_{\{|X_n|\leq c_n\}}$ and of $\sum X_n$ vs $\sum X_nI_{\{|X_n|\leq c_n\}}$

score 160 · Answer 1 · 2016-11-01 09:50:36

160

Views

Pointwise convergence of $X_n$ vs $X_nI_{\{|X_n|\leq c_n\}}$ and of $\sum X_n$ vs $\sum X_nI_{\{|X_n|\leq c_n\}}$

Published on 01 Nov 2016 - 9:50

score 88 · Answer 2 · 2016-11-04 11:30:41

88

Views

this is the hard problem in real analysis by bruckner, i dont solve it.

Published on 04 Nov 2016 - 11:30

score 65 · Answer 3 · 2016-11-04 15:56:35

65

Views

let$\{f_n\}$ be a sequence of Lebesgue measurable functions on $[0,\infty)$ suth that $\vert {f_n (x)}\vert \le e^{-x}$

Published on 04 Nov 2016 - 15:56

score 160 · Answer 4 · 2016-11-07 04:46:17

160

Views

Stable Distribution of Random Variables

Published on 07 Nov 2016 - 4:46

score 425 · Answer 5 · 2016-11-13 18:49:02

425

Views

Prove/Disprove $E[X|\mathscr G] = X$ if $X$ is almost surely constant.

Published on 13 Nov 2016 - 18:49

score 57 · Answer 6 · 2016-11-14 15:39:22

57

Views

Question about a particular example of $X_n \to_p X$ but $X_n \nrightarrow_{as} X$

Published on 14 Nov 2016 - 15:39

score 172 · Answer 7 · 2016-11-15 22:32:57

172

Views

Show that $ {S_n\over 2^.5(logn)} $ converges to 0 almost surely.

Published on 15 Nov 2016 - 22:32

score 475 · Answer 8 · 2016-11-22 10:19:16

475

Views

Why does $f_n \to 0$ almost everywhere?

Published on 22 Nov 2016 - 10:19

score 629 · Answer 9 · 2016-11-28 21:42:48

629

Views

Question in proof of Glivenko-Cantelli Theorem

Published on 28 Nov 2016 - 21:42

score 617 · Answer 10 · 2016-12-03 17:00:10

617

Views

If $X_{n} \to X$ in probability, then for every subsequence there exists a further subsequence...

Published on 03 Dec 2016 - 17:00

score 665 · Answer 11 · 2016-12-05 21:45:38

665

Views

If $\mathbb{E}\left(g(X)\mid\mathscr{G}\right) = g(Y)$ a.s. for each bounded measurable function $g$, then $X=Y$ a.s.?

Published on 05 Dec 2016 - 21:45

score 220 · Answer 12 · 2026-02-23 13:41:33

220

Views

Prove that $ \frac{d\nu}{d\lambda}=\frac{d\nu}{d\mu}\cdot \frac{d\mu}{d\lambda},\text{ } \lambda\text{-a.e.} $

Published on 23 Feb 2026 - 13:41

score 2.9k · Answer 13 · 2016-12-11 22:55:00

2.9k

Views

Almost sure and Probability Convergence of the Maximum of I.I.D. Random Variables

Published on 11 Dec 2016 - 22:55

score 49 · Answer 14 · 2016-12-13 20:38:46

49

Views

Show: $f_n \to f, a.e. \Rightarrow F_n(x) := \int_{(-\infty, x]}{f_n d\lambda^1} \to F_0$

Published on 13 Dec 2016 - 20:38

score 53 · Answer 15 · 2016-12-14 09:26:25

53

Views

Show: $\int_{[a,b]}{f d\lambda^d}=0 \:\:\:\:\forall a, b \in \Bbb R ^d \:\:\mathrm{ with }\:\: a \le b\Rightarrow f=0 \:\:\mathrm{ a.e.}$

Published on 14 Dec 2016 - 9:26

List Question

Pointwise convergence of $X_n$ vs $X_nI_{\{|X_n|\leq c_n\}}$ and of $\sum X_n$ vs $\sum X_nI_{\{|X_n|\leq c_n\}}$

this is the hard problem in real analysis by bruckner, i dont solve it.

let$\{f_n\}$ be a sequence of Lebesgue measurable functions on $[0,\infty)$ suth that $\vert {f_n (x)}\vert \le e^{-x}$

Stable Distribution of Random Variables

Prove/Disprove $E[X|\mathscr G] = X$ if $X$ is almost surely constant.

Question about a particular example of $X_n \to_p X$ but $X_n \nrightarrow_{as} X$

Show that $ {S_n\over 2^.5(logn)} $ converges to 0 almost surely.

Why does $f_n \to 0$ almost everywhere?

Question in proof of Glivenko-Cantelli Theorem

If $X_{n} \to X$ in probability, then for every subsequence there exists a further subsequence...

If $\mathbb{E}\left(g(X)\mid\mathscr{G}\right) = g(Y)$ a.s. for each bounded measurable function $g$, then $X=Y$ a.s.?

Prove that $ \frac{d\nu}{d\lambda}=\frac{d\nu}{d\mu}\cdot \frac{d\mu}{d\lambda},\text{ } \lambda\text{-a.e.} $

Almost sure and Probability Convergence of the Maximum of I.I.D. Random Variables

Show: $f_n \to f, a.e. \Rightarrow F_n(x) := \int_{(-\infty, x]}{f_n d\lambda^1} \to F_0$

Show: $\int_{[a,b]}{f d\lambda^d}=0 \:\:\:\:\forall a, b \in \Bbb R ^d \:\:\mathrm{ with }\:\: a \le b\Rightarrow f=0 \:\:\mathrm{ a.e.}$

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