Tagged Questions
0
votes
1answer
80 views
p-lim inf definition (limit inferior in probability)
For an arbitrary sequence of real-valued random variables $\{Z_n\}_1^\infty$ , we define limit inferior in probability as follow :
$$ p-\liminf_{n\to \infty} Z_n \equiv \sup \{ \beta|\lim_{n\to ...
1
vote
2answers
119 views
Entropy expression optimization with Langrange multipliers
I have recently encountered variants of the following expression:
\begin{equation}
S = H(a,b,c,d)-H(a+b,c+d)
\end{equation}
where $H$ is the Shannon entropy function, that is $H(X)=\sum_{x\in X}-x\log ...
2
votes
2answers
92 views
Numbers which encode other numbers infinite times.
Let $g(x,n)$ be a function which chops off the first n digits of the binary decimal expansion of x.
eg $g(0.1010111,2)=0.10111$
Is there a function $f(x)$ from the reals to the reals, such that for ...
