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Jun
30
awarded  Popular Question
Jun
28
accepted Mutual information of discrete RVs which converge in distribution to a continuous RV
Jun
26
comment Mutual information of discrete RVs which converge in distribution to a continuous RV
The statement, as I have made it is probably FALSE because convergence in distribution is too WEAK to prove convergence of expectation for operations as poorly behaved as mutual information.
Jun
23
revised Mutual information of discrete RVs which converge in distribution to a continuous RV
deleted 148 characters in body; edited tags
Jun
23
comment Limit of integrals of simple functions over a finite measure
For any measurable $A$, then $\mu_n(A)\rightarrow \mu(A)$
Jun
23
revised Limit of integrals of simple functions over a finite measure
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Jun
23
asked Limit of integrals of simple functions over a finite measure
Jun
23
accepted If $X$ has a density, then does $Y:=g(X)\cdot 1_{\{X>0\}}$? (No…?)
Jun
23
accepted Anywhere I integrate $f_n$, the integral approaches $f$. Is $\lim_n f_n = f$ a.e.?
Jun
23
comment Anywhere I integrate $f_n$, the integral approaches $f$. Is $\lim_n f_n = f$ a.e.?
Wow this is awful. Thank you for the response. So I guess my contradiction comes when I say that $\int_S f_n-f \rightarrow 0 \Rightarrow \int_S |f_n-f| \rightarrow 0...$
Jun
23
comment Anywhere I integrate $f_n$, the integral approaches $f$. Is $\lim_n f_n = f$ a.e.?
Why the downvote!
Jun
23
revised Anywhere I integrate $f_n$, the integral approaches $f$. Is $\lim_n f_n = f$ a.e.?
deleted 4 characters in body; edited tags
Jun
23
revised Anywhere I integrate $f_n$, the integral approaches $f$. Is $\lim_n f_n = f$ a.e.?
added 105 characters in body
Jun
23
asked Anywhere I integrate $f_n$, the integral approaches $f$. Is $\lim_n f_n = f$ a.e.?
Jun
22
revised Mutual information of discrete RVs which converge in distribution to a continuous RV
deleted 224 characters in body
Jun
22
revised Mutual information of discrete RVs which converge in distribution to a continuous RV
deleted 187 characters in body
Jun
22
revised Mutual information of discrete RVs which converge in distribution to a continuous RV
edited tags; edited title
Jun
22
comment Mutual information of discrete RVs which converge in distribution to a continuous RV
This is an interesting idea, although it is worrying in that we now have something that is non-negative (discrete entropy) converging to something that could possibly be negative (differential entropy). In the application, I contrived the use of mutual information because it represents the same quantity in both continuous and discrete cases.
Jun
21
comment Using a sequence of measures to create simple functions which approximate the Radon-Nikodym derivative of the limiting measure
@3дравыйСмысл Truthfully, it is the part that is missing for me to answer my real question: math.stackexchange.com/questions/1330989 $${}$$ in short, this is to prove that 'The mutual information between estimates of two RVs approaches the mutual information between the source RVs'. In information theory terms, this is a completely intuitive/plausible result. It's just that technicalities arise in the framework...
Jun
19
asked Using a sequence of measures to create simple functions which approximate the Radon-Nikodym derivative of the limiting measure