2
votes
0answers
33 views

Where to read about this kind of “measure of irredundancy” of a set from a family of sets?

Studying a very practical problem from psychometrics, I encountered the following construction. Let $(X,\mu)$ be a measure space; if preferred, you can presume $\mu$ is a probability measure. In any ...
6
votes
3answers
382 views

Signal Processing reference for pure mathematician

Before giving a more detailed question below, the basic one is: can anyone recommend a good signal-processing reference which would be maximally readable by a pure mathematician (who nevertheless ...
4
votes
1answer
497 views

Non-trivial consequences of Lob's theorem

Informally, Löb's theorem (Wikipedia, PlanetMath) shows that: a mathematical system cannot assert its own soundness without becoming inconsistent [Yudkowsky] In symbols: if $PA\vdash$ ...
12
votes
3answers
819 views

Applications of and motivation for von Neumann's mean ergodic theorem

I stated von Neumann's mean ergodic theorem (VNMET) in a talk recently and someone in the audience asked what it was good for. The only application I knew of VNMET was to prove Birkhoff's ergodic ...
3
votes
3answers
1k views

Why are divisible abelian groups important?

I just quote wikipedia: "Divisible groups are important in understanding the structure of abelian groups, especially because they are the injective abelian groups." I am asking for detail ...