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