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Jul
16
revised Easiest way to find the 'area of a Venn diagram,' given certain information.
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Jul
16
comment Easiest way to find the 'area of a Venn diagram,' given certain information.
We can do it iteratively. $V(X_1)$ is known. Now for each $n,$ it is easy to see that: $$V(\cup_{i=1}^n X_i)=V(\cup_{i=1}^{n-1}X_i)+V(X_n)-V\left((\cup_{i=1}^{n-1}X_i)\cap X_n\right).$$
Jul
16
awarded  Custodian
Jul
16
reviewed Approve Easiest way to find the 'area of a Venn diagram,' given certain information.
Jul
16
revised Easiest way to find the 'area of a Venn diagram,' given certain information.
edited title
Jul
16
awarded  Peer Pressure
Jul
16
comment Easiest way to find the 'area of a Venn diagram,' given certain information.
I already know about the standard inequality using the inclusion-exclusion principle, but in this formula all the terms with more than one intersection in $V(\dots)$ need to be further broken up, creating a big mess. I am going to code this up so I have motivation to find one with few and easily enumerable terms.
Jul
16
asked Easiest way to find the 'area of a Venn diagram,' given certain information.
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
added 145 characters in body
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