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5 votes
3 answers
112 views

The number of binary strings of length $n$ without the sequence (1;0;1) in it. [duplicate]

4 votes
1 answer
118 views

Proof: All functions in $L^2[0,1]$ are in $L^1[0,1]$

4 votes
2 answers
147 views

Exemple where tower property of conditional expectation is NOT verify

3 votes
3 answers
206 views

Proof: How many continuous/bounded functions on $[0,1]$ verify $f(x)=f(x/2)\frac{1}{\sqrt{2}}$?

3 votes
1 answer
54 views

Proof:$X_n\overset{a.s}{\rightarrow}X,Y_n\overset{a.s}{\rightarrow}Y \Rightarrow X_n+Y_n\overset{a.s.}{\rightarrow}X+Y$

2 votes
0 answers
112 views

Proof: $C^\infty[0,1]$ is dense in $L^1[0,1]$

2 votes
1 answer
31 views

Definition of $L_2(\Omega \times [0,T])$ - Stochastic Processes-

2 votes
2 answers
51 views

Question about demonstration of the type $A\Leftrightarrow B$

1 vote
0 answers
37 views

Proof: $S$ a subset of $l^2(\mathbb{N})$ is a closed subset

1 vote
0 answers
35 views

Proove verification: $\int_{0}^{1}I_{\omega \notin \mathbb{Q}}(w) d\mathbb{P(\omega )}=1$ using Borel Cantelli lemma

1 vote
1 answer
87 views

Algorithm verification: Get all the combinations of possible words

1 vote
0 answers
38 views

If $X_n(\omega )\overset{L^2}{\rightarrow}X(\omega )$ and g(x) is continuous and bounded so $g(X_n(\omega ))\overset{a.s.}{\rightarrow}g(X(\omega ))$

1 vote
0 answers
40 views

Point wise convergence does not imply convergence in $L^p$ -example-

0 votes
1 answer
85 views

How can you proove that every bounded function in $L^1[0;1]$ can be approximated by continuous function in $C[0;1]$?

0 votes
0 answers
20 views

Does all the possible unions of (no) countable element from a no countable partition of a set define a $\sigma$ algebra