diff --git a/Analysis/MeasureTheory/Section_1_4_2.lean b/Analysis/MeasureTheory/Section_1_4_2.lean index 6a7339b2..a4e024cd 100644 --- a/Analysis/MeasureTheory/Section_1_4_2.lean +++ b/Analysis/MeasureTheory/Section_1_4_2.lean @@ -154,7 +154,7 @@ theorem BorelSigmaAlgebra.generated_by_boxes (d:ℕ) : BorelSigmaAlgebra (Euclid theorem BorelSigmaAlgebra.generated_by_elementary (d:ℕ) : BorelSigmaAlgebra (EuclideanSpace' d) = ConcreteSigmaAlgebra.generated_by { E : Set (EuclideanSpace' d) | IsElementary E } := by sorry open Ordinal in -/-- Exercise 1.4.15 (Recursive definition of generated sigma-algebra)-/ +/-- Exercise 1.4.15 (Recursive definition of generated sigma-algebra). -/ def ConcreteSigmaAlgebra.generated_by_eq {X:Type*} (F: Set (Set X)) : (ConcreteSigmaAlgebra.generated_by F).measurableSets = ⋃ α < ω₁, @@ -181,7 +181,7 @@ theorem BorelSigmaAlgebra.prod {d₁ d₂:ℕ} {E : Set (EuclideanSpace' d₁)} := by sorry -/-- Exercise 1.4.18(i) -/ +/-- Exercise 1.4.18(i) (slice along first factor). -/ theorem BorelSigmaAlgebra.slice_fst {d₁ d₂:ℕ} {E : Set (EuclideanSpace' (d₁+d₂))} (hE: (BorelSigmaAlgebra (EuclideanSpace' (d₁+d₂))).measurable E) (x₂ : EuclideanSpace' d₂ ) : @@ -189,7 +189,7 @@ theorem BorelSigmaAlgebra.slice_fst {d₁ d₂:ℕ} {E : Set (EuclideanSpace' (d := by sorry -/-- Exercise 1.4.18(i) -/ +/-- Exercise 1.4.18(i) (slice along second factor). -/ theorem BorelSigmaAlgebra.slice_snd {d₁ d₂:ℕ} {E : Set (EuclideanSpace' (d₁+d₂))} (hE: (BorelSigmaAlgebra (EuclideanSpace' (d₁+d₂))).measurable E) (x₁ : EuclideanSpace' d₁ ) :