mathlib

3594b635 - feat(probability_theory/independence): if a family of pi-systems is independent, then so are the generated measurable spaces (#9387)

feat(probability_theory/independence): if a family of pi-systems is independent, then so are the generated measurable spaces (#9387) The main result in this PR is `Indep_sets.Indep`: if π-systems are independent as sets of sets, then the measurable space structures they generate are independent. We already had a version of this for two pi-systems instead of a family. In order to prove this, and as preparation for a next PR about Kolmogorov's 0-1 law, a definition `pi_Union_Inter` is introduced to build a particular pi-system from a family of pi-systems. Co-authored-by: Rémy Degenne <remydegenne@gmail.com> Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr>