Theorems · Theorem · measure theory

MeasureTheory.IsProjectiveMeasureFamily.eq_zero_of_isEmpty

∀ {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)} [h : IsEmpty ((i : ι) → α i)],
  MeasureTheory.IsProjectiveMeasureFamily P → ∀ (I : Finset ι), P I = 0

Defined in: Mathlib.MeasureTheory.Constructions.Projective
Cited by: 2 results in Mathlib
Foundations: Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasurableSpace IsEmpty

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Cites11

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

Finsetstatement and proof · cited by 13,712
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
MeasureTheory.Measure.mapproof · cited by 858
IsEmptystatement and proof · cited by 759
Finset.restrict₂proof · cited by 44
Finset.subset_insertproof · cited by 36
MeasureTheory.IsProjectiveMeasureFamilystatement and proof · cited by 27
MeasureTheory.Measure.map_zeroproof · cited by 17
MeasureTheory.Measure.eq_zero_of_isEmptyproof · cited by 7
isEmpty_piproof · cited by 4

Cited by2

Results whose statement or proof uses this declaration.

MeasureTheory.IsProjectiveMeasureFamily.congr_cylinder_of_subsetproof · cited by 1
MeasureTheory.projectiveFamilyFun_unionproof · cited by 0