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Theorems · Theorem · measure theory

MeasureTheory.extend_empty

∀ {α : Type u_1} {P : Set α → Prop} {m : (s : Set α) → P s → ENNReal} (P0 : P ∅),
  m ∅ P0 = 0 → MeasureTheory.extend m ∅ = 0
Defined in
Mathlib.MeasureTheory.OuterMeasure.Induced
Cited by
1 results in Mathlib
Foundations
Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.inducedOuterMeasure · cited by 22MeasureTheory.inducedOute…MeasureTheory.extend_iUnion · cited by 2MeasureTheory.extend_iUni…Set · cited by 53352SetENNReal · cited by 9879ENNRealMeasureTheory.extend · cited by 24MeasureTheory.extendMeasureTheory.extend_eq · cited by 10MeasureTheory.extend_eqMeasureTheory.extend_emptyCITED BYCITES

Cites4

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Cited by2

Results whose statement or proof uses this declaration.