Foliation ergodic theory
- Ambrose Kakutani (in particular, question 39)
- Does mixing make any sense? (use category, differentiability, $C^\infty$, analytic structure)
- Averaging procedure difficulties:
- ergodic theorems, existence of invariant measures, ergodic decomposition, unique ergodicity and uniform convergence.
- polynomial growth ...
- Look at some specific foliations
- Plante's stuff on connections with homology
- Does pointwise entropy make sense?