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fpvandoorn committed Aug 26, 2020
1 parent 4893c8a commit db56db0
Showing 1 changed file with 4 additions and 6 deletions.
10 changes: 4 additions & 6 deletions src/measure_theory/borel_space.lean
Original file line number Diff line number Diff line change
Expand Up @@ -550,16 +550,14 @@ borel_eq_generate_from_of_subbasis is_topological_basis_Ioo_rat.2.2
lemma measure_ext_Ioo_rat {μ ν : measure ℝ} [locally_finite_measure μ]
(h : ∀ a b : ℚ, μ (Ioo a b) = ν (Ioo a b)) : μ = ν :=
begin
apply measure.ext_of_generate_from_of_cover_same borel_eq_generate_from_Ioo_rat,
refine measure.ext_of_generate_from_of_cover_subset borel_eq_generate_from_Ioo_rat _ _
(subset.refl _) _ _ _,
{ exact countable_Union (λ a, (countable_encodable _).bUnion $ λ _ _, countable_singleton _) },
{ simp only [mem_Union, mem_singleton_iff],
rintros _ ⟨a₁, b₁, h₁, rfl⟩ _ ⟨a₂, b₂, h₂, rfl⟩ ne,
{ simp only [is_pi_system, mem_Union, mem_singleton_iff],
rintros _ _ ⟨a₁, b₁, h₁, rfl⟩ ⟨a₂, b₂, h₂, rfl⟩ ne,
simp only [Ioo_inter_Ioo, sup_eq_max, inf_eq_min, ← rat.cast_max, ← rat.cast_min, nonempty_Ioo] at ne ⊢,
refine ⟨_, _, _, rfl⟩,
assumption_mod_cast },
{ simp only [mem_Union, mem_singleton_iff],
rintros _ ⟨a, b, h, rfl⟩,
exact is_measurable_Ioo },
{ exact is_topological_basis_Ioo_rat.2.1 },
{ simp only [mem_Union, mem_singleton_iff],
rintros _ ⟨a, b, h, rfl⟩,
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