Theorems · Theorem · measure theory

MeasureTheory.SignedMeasure.exists_subset_restrict_nonpos

∀ {α : Type u_1} [inst : MeasurableSpace α] {s : MeasureTheory.SignedMeasure α} {i : Set α},
  s i < 0 →
    ∃ j,
      MeasurableSet j ∧
        j ⊆ i ∧ MeasureTheory.VectorMeasure.restrict s j ≤ MeasureTheory.VectorMeasure.restrict 0 j ∧ s j < 0

A measurable set of negative measure has a negative subset of negative measure.

Defined in: Mathlib.MeasureTheory.VectorMeasure.Decomposition.Hahn
Cited by: 1 results in Mathlib
Foundations: Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasurableSpace

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Cited by1

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MeasureTheory.SignedMeasure.exists_compl_positive_negativeproof · cited by 2