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Nov
12
asked About the Alon-Krivilevich-Vu result on concentration of eigenvalues of random matrices.
Nov
11
revised About the “Bounded Convergence Theorem”
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Nov
9
comment About the “Bounded Convergence Theorem”
But "dominated convergence theorem" is a separate theorem - right? I amtalking of the "bounded convergece theorem". Is my understanding of the definition of "uniformly bounded" correct as stated in point 1? you have examples of the kind I am looking for in the third point?
Nov
8
comment About the “Bounded Convergence Theorem”
Any example you have in mind? (So you are saying that uniform convergence is not a necessary condition) But is your example then satisfying the "bounded convergence theorem" conditions?
Nov
8
comment About the “Bounded Convergence Theorem”
Can you kindly explain a bit more?
Nov
8
asked About the “Bounded Convergence Theorem”
Oct
30
comment Why is probability a measure?
I guess the way to make sense of the RHS is to say that $\int dP$ is $\int 1 dP$ and now since $1$ is a bounded measurable function one can write it as as the limit of a sums of ``simple" functions which can be chosen as indicator functions over some $n-$partition say $\{ A_i \}_{i=1}^{n}$ of the set $\vert X - a \vert > b$ and then one would have $\int_{ \vert X - a \vert > b} dP =lim _{n \rightarrow \infty} \sum_{i=1}^n P(A_i)$. (where implcitly we are choosing a different A-partiton for each $n$ and these choices do not matter) Right?
Oct
28
comment Why is probability a measure?
For the LHS to make sense isn't $P$ a real valued map on a Borel algebra of sets in the sample space which is $X$'s domain?
Oct
28
asked Why is probability a measure?
Oct
15
comment About calculating limits of integrals (Part 2)
Your answer doesn't look right : The answer to the integral is $2\pi i (Res_{z = i/2} [z\tanh (\pi z) \log(z^2+a^2) ] )$ The only one having a pole is the $tanh$ part and $Res_{z = i/2} [ tanh (\pi z) ] = 1/\pi$. So the answer to the integral is $(2\pi i )*(i/2)*(1/\pi)*\log (a^2 - 1/4 ) = - log(a^2 - 1/4)$
Oct
14
comment About calculating limits of integrals (Part 2)
Can you explain how you took this limit to show that $\frac{z - i/2}{cosh (\pi z ) } \rightarrow \frac{1}{\pi sinh (\pi i/2) }$ ?
Oct
13
comment About calculating limits of integrals (Part 2)
I am not vouching for my Mathematica answer. I don't trust my Mathematica skills :D I would be delighted if someone could check what is the answer on Mathematica!
Oct
13
comment About calculating limits of integrals (Part 2)
Could you kindly explain as to what you mean by saying that ``$log z$ is the principal branch"? (Does it mean the same as my way of specifying where I am choosing to put my branch-cuts?)
Oct
12
comment About calculating limits of integrals (Part 2)
Imagine that the branchcut of the function $log(z^2 + a^2)$ is taken to start at $\pm ia$ and goes up/down the $y-$axis. Also you can assume that the point $i(n+\frac{1}{2})$ is between the points $\pm ia$.
Oct
12
revised About calculating limits of integrals (Part 2)
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Oct
12
revised About calculating limits of integrals (Part 2)
added 12 characters in body
Oct
12
asked About calculating limits of integrations (Part 3)
Oct
12
revised About calculating limits of integrals (Part 1)
edited title
Oct
12
asked About calculating limits of integrals (Part 2)
Oct
11
revised Can I get multivariable taylor series expansion on wolfram alpha or matlab?
added 10 characters in body; edited tags; edited title