Theorems · Theorem · measure theory

MeasureTheory.IsProjectiveMeasureFamily.congr_cylinder

∀ {ι : Type u_1} {α : ι → Type u_2} [inst : (i : ι) → MeasurableSpace (α i)]
  {P : (J : Finset ι) → MeasureTheory.Measure ((j : ↥J) → α ↑j)} {I J : Finset ι},
  MeasureTheory.IsProjectiveMeasureFamily P →
    ∀ {S : Set ((i : ↥I) → α ↑i)} {T : Set ((i : ↥J) → α ↑i)},
      MeasurableSet S → MeasurableSet T → MeasureTheory.cylinder I S = MeasureTheory.cylinder J T → (P I) S = (P J) T

Defined in: Mathlib.MeasureTheory.Constructions.Projective
Cited by: 1 results in Mathlib
Foundations: Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasurableSpace

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Cites16

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Setstatement and proof · cited by 53,352
Finsetstatement and proof · cited by 13,712
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ENNRealstatement · cited by 9,879
Set.preimageproof · cited by 4,946
MeasurableSetstatement and proof · cited by 3,075
Set.inter_selfproof · cited by 63
Finset.subset_union_leftproof · cited by 59
MeasureTheory.cylinderstatement and proof · cited by 49
Finset.subset_union_rightproof · cited by 45

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.projectiveFamilyFun_congrproof · cited by 3