Theorems · Theorem · measure theory

MeasureTheory.projectiveFamilyContent_sdiff_of_subset

∀ {ι : Type u_1} {α : ι → Type u_2} {mα : (i : ι) → MeasurableSpace (α i)}
  {P : (J : Finset ι) → MeasureTheory.Measure ((j : ↥J) → α ↑j)} {s t : Set ((i : ι) → α i)}
  [∀ (J : Finset ι), MeasureTheory.IsFiniteMeasure (P J)] (hP : MeasureTheory.IsProjectiveMeasureFamily P),
  s ∈ MeasureTheory.measurableCylinders α →
    t ∈ MeasureTheory.measurableCylinders α →
      t ⊆ s →
        (MeasureTheory.projectiveFamilyContent hP) (s \ t) =
          (MeasureTheory.projectiveFamilyContent hP) s - (MeasureTheory.projectiveFamilyContent hP) t

Defined in

Mathlib.MeasureTheory.Constructions.ProjectiveFamilyContent

Cited by

1 results in Mathlib

Foundations

Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.IsFiniteMeasure