MeasureTheory.Measure.exists_isOpen_everywherePosSubset_eq_diff

theorem MeasureTheory.Measure.exists_isOpen_everywherePosSubset_eq_diff : ∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : MeasurableSpace α] (μ : MeasureTheory.Measure α) (s : Set α), ∃ u, IsOpen u ∧ μ.everywherePosSubset s = s \ u

This theorem states that, for any topological space `α` with the associated measurable space, and any measure `μ` and set `s` of type `α`, there exists an open set `u` such that the everywhere positive subset of `s` with respect to the measure `μ` is equivalent to the set difference of `s` and `u`. In other words, you can obtain the everywhere positive subset of `s` by removing an open set `u` from `s`.

More concisely: For any topological space `α` with a measurable structure, measure `μ`, and set `s` of type `α`, there exists an open set `u` such that `s \ u` is equivalent to the everywhere positive subset of `s` with respect to `μ`.