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Sep
25
comment If $S \in L(X,Y)$ and lim$_{r \to 0}\frac{\|Sr\|}{\|r\|}=0$,then $S=0$.
Because Su=0 is obvious if u=0 and because ||Su||/||u|| does not exist if u=0.
Sep
25
comment Question on sigma additivity on an algebra.
Being sigma-additive on an algebra $F$ means that, for every disjoint sequence $(A_n)$ in $F$ such that the union $A=\bigcup\limits_nA_n$ is in $F$ then $P(A)=\sum\limits_nP(A_n)$. Hence your "major concern" is moot.
Sep
25
answered Joint distribution of two gaussians, one of which is dependent on the other.
Sep
25
revised Continuity of $xy^3/(x^2+y^6)$ at $(x,y)=(0,0)$
edited title
Sep
25
revised Finding the general term of two related recurrence relations
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Sep
24
comment Random variable stochastic bigger than random variable
And if there is no probability density function?
Sep
24
awarded  Autobiographer
Sep
24
awarded  Good Answer
Sep
24
revised Proving a theorem about covariance matrix
added 18 characters in body
Sep
24
revised For every $x\in\mathbb R$ and $\varepsilon$ > 0 , there exist $\,q,q'\in\mathbb Q$, such that $q<x<q'$ and $\left |q-q' \right |< \varepsilon$
added 85 characters in body
Sep
24
comment Uncommon question for everyone that is related to mathematics
Why uncommon? Especially for everyone that is related to mathematics...
Sep
24
revised The set of points in complex plane that satisfy a strict linear inequality is open
added 5 characters in body
Sep
24
revised how to integrate $\sqrt{1-x^{2/3}}$
added 41 characters in body
Sep
24
answered how to integrate $\sqrt{1-x^{2/3}}$
Sep
24
revised The set of points in complex plane that satisfy a strict linear inequality is open
edited tags
Sep
24
answered The set of points in complex plane that satisfy a strict linear inequality is open
Sep
24
comment What kind of f(n)'s make the limsup statement is true? What kind don't?
Necessary and sufficient condition: $f(n)\to\infty$ when $n\to\infty$.
Sep
24
answered On “for all” in if and only if statements in probability theory and stochastic calculus
Sep
24
comment Joint distribution of range $(R=X_n-X_1)$ and mid-range $(V=\frac{1}{2}(X_1+X_n)$order statistics
Since $(R,V)$ is a linear transform of $U=(X_{(1)},X_{(n)})$, it is enough to determine he distribution of $U$. And this distribution is well known...
Sep
24
comment Prove variance inequality given conditional expectation
Are you sure about the implication? See answer below.