On computing measures of open sets of trees

Since Gogacz et al. proved that regular languages of infinite trees are universally measurable, 

the problem of computing a measure of a given regular set became an appealing and, it seems, difficult problem.

 

Up to now, only ``simple'' cases were solved:

either when the structure of the automaton is intrinsically deterministic or when the set enjoys some locality properties.

 

In this talk, I will formulate the problem, recall old results, and solve the ``closed'' case, i.e.

I will show how to compute the measure of a given closed regular set of infinite trees.