List questions from almost-everywhere

Published on 08 Dec 2015 - 2:38

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If $X_1,\ldots X_n$ are iid random variables with $E(X_{i}) = 0$ and $E(X_{i}^2) = 1$, then $\frac{\sum_{i=1}^{n}X_i^2}{n} \to E(X_i^2)$?

Published on 15 Dec 2015 - 8:25

1.4k

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Almost sure and $L_1$ convergence to different limits?

Published on 22 Dec 2015 - 18:10

101

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Almost sure convergence of sum

Published on 11 Jan 2016 - 14:11

209

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Conditional probability and almost sure equality confusion

Published on 25 Jan 2016 - 11:09

67

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Almost everywhere equality of r.v.'s , based on information on mean values.

Published on 29 Jan 2016 - 7:16

533

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Infinite sum of indicators almost sure convergence

Published on 29 Jan 2016 - 23:17

229

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Does $\mathbb{P}$-a.s. convergence preserve independence?

Published on 08 Feb 2016 - 11:21

266

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If $X_n\geq 0,~X_n\rightarrow X$ ae and $E(X_n)\leq c,$ then $E(X)\leq c.$

Published on 09 Feb 2016 - 20:50

1k

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If $X_n\nearrow X$ then $E(X_n)\rightarrow E(X)$?

Published on 10 Feb 2016 - 1:07

135

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$ \lim\limits_{n\rightarrow \infty} {\frac{B_{t}}{t}}$ Brownian Motion

Published on 11 Feb 2016 - 15:05

2.9k

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Almost sure convergence along a subsequence implies convergence in probability over the whole sequence

Published on 15 Feb 2016 - 15:10

51

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If the cdf of $X$ is $I_{[a,+\infty)}$ then $P(X=a)=1.$

Published on 16 Feb 2016 - 1:48

186

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$f:[a,b] \to \mathbb R$ continuous a.e. , is there a sequence of functions of finite discontinuity on $[a,b]$ converging uniformly to $f$ on $[a,b]$?

Published on 17 Feb 2016 - 14:38

224

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Cardinality of almost everywhere continuous functions

Published on 21 Feb 2016 - 16:01

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Strong Law of Large Numbers converge a.s.

If $X_1,\ldots X_n$ are iid random variables with $E(X_{i}) = 0$ and $E(X_{i}^2) = 1$, then $\frac{\sum_{i=1}^{n}X_i^2}{n} \to E(X_i^2)$?

Almost sure and $L_1$ convergence to different limits?

Almost sure convergence of sum

Conditional probability and almost sure equality confusion

Almost everywhere equality of r.v.'s , based on information on mean values.

Infinite sum of indicators almost sure convergence

Does $\mathbb{P}$-a.s. convergence preserve independence?

If $X_n\geq 0,~X_n\rightarrow X$ ae and $E(X_n)\leq c,$ then $E(X)\leq c.$

If $X_n\nearrow X$ then $E(X_n)\rightarrow E(X)$?

$ \lim\limits_{n\rightarrow \infty} {\frac{B_{t}}{t}}$ Brownian Motion

Almost sure convergence along a subsequence implies convergence in probability over the whole sequence

If the cdf of $X$ is $I_{[a,+\infty)}$ then $P(X=a)=1.$

$f:[a,b] \to \mathbb R$ continuous a.e. , is there a sequence of functions of finite discontinuity on $[a,b]$ converging uniformly to $f$ on $[a,b]$?

Cardinality of almost everywhere continuous functions

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