mathlib3
cd884eb8 - feat(measure_theory): finite_spanning_sets_in (#4668)

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5 years ago
feat(measure_theory): finite_spanning_sets_in (#4668) * We define a new Type-valued structure `finite_spanning_sets_in` which consists of a countable sequence of sets that span the type, have finite measure, and live in a specified collection of sets, * `sigma_finite` is redefined in terms of `finite_spanning_sets_in` * One of the ext lemmas is now conveniently formulated in terms of `finite_spanning_sets_in` * `finite_spanning_sets_in` is also used to remove a little bit of code duplication in `prod` (which occurred because `sigma_finite` was a `Prop`, and forgot the actual construction) * Define a predicate `is_countably_spanning` which states that a collection of sets has a countable spanning subset. This is useful for one particular lemma in `prod`. * Generalize some lemmas about products in the case that the σ-algebras are generated by a collection of sets. This can be used to reason about iterated products. * Prove `prod_assoc_prod`. * Cleanup in `measurable_space` and somewhat in `measure_space`. * Rename `measurable.sum_rec -> measurable.sum_elim` (and give a different but definitionally equal statement)
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