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fix: Ex. 1.4.18(i) slice_fst/slice_snd labels #564

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fix: Ex. 1.4.18(i) slice_fst/slice_snd labels #564

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6 changes: 3 additions & 3 deletions Analysis/MeasureTheory/Section_1_4_2.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -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,
Expand All @@ -181,15 +181,15 @@ 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 ) :
(BorelSigmaAlgebra (EuclideanSpace' d₁)).measurable { x₁ | (EuclideanSpace'.prod_equiv d₁ d₂).symm ⟨ x₁, x₂ ⟩ ∈ E }
:=
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 ) :
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