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seen Apr 16 at 0:52

Apr
16
answered The Lebesgue Integral and the Dirichlet function
Apr
15
answered Piece-Wise Function
Apr
15
answered Prove the probability of n events intersecting
Apr
15
answered Prove that (integer + non-integer) never equals an integer.
Apr
15
answered $ (1-x)^2\sum_{N+1}^\infty (n+1)x^n = x^{n+1}(n+2 - (n+1)x) $ small independent of $x\in (0,1)$?
Apr
6
accepted Bounding the solution of a wave equation in 3 dimensions
Apr
6
answered Bounding the solution of a wave equation in 3 dimensions
Apr
6
accepted Proof of uniqueness of the extension in Kolmogorov extension theorem
Apr
4
asked Conditional expectation of a continuous random variable
Jan
11
comment Proof of uniqueness of the extension in Kolmogorov extension theorem
Right, I don't know how it didn't occur to me.
Jan
11
asked Proof of uniqueness of the extension in Kolmogorov extension theorem
Jan
7
comment How to see that separable metric space can be covered in a specific way?
Thanks, that makes it even easier
Jan
7
comment How to see that separable metric space can be covered in a specific way?
Since ${x_m} \in K\left( {{x_m},\frac{1}{n}} \right)$, I can conclude that $\left\{ {{x_m} \in S:m \in \mathbb{N}} \right\} \subseteq \left\{ {K\left( {x,\frac{1}{n}} \right):x \in \left\{ {{x_m} \in S:m \in \mathbb{N}} \right\}} \right\}$. It follows that $S = \overline {\left\{ {{x_m} \in S:m \in \mathbb{N}} \right\}} \subseteq \overline {\left\{ {K\left( {x,\frac{1}{n}} \right):x \in \left\{ {{x_m} \in S:m \in \mathbb{N}} \right\}} \right\}} $ from which the statement easily follows. Thanks
Jan
7
asked How to see that separable metric space can be covered in a specific way?
Jan
5
awarded  Yearling
Dec
21
awarded  Tumbleweed
Dec
16
comment To check $(0,1)$ is open in $(0,1] $ or not
Subspace topology is defined as an intersection of the given subset with all open sets in the original set. Since $\left( {0,1} \right)$ is open in $\mathbb{R}$, the answer becomes obvious
Dec
16
revised Conditional Expectation of a random variable with itself
Deleted the redundant part of the question
Dec
15
suggested suggested edit on Conditional Expectation of a random variable with itself
Dec
15
comment Conditional Expectation of a random variable with itself
Notation $\mathcal{G}$ for a sigma-algebra is pretty common and it is as relevant to the rest of the question as the appendix is to a human. I've suggested the part to be removed