Theorems · Theorem · measure theory

MeasureTheory.Measure.ae_rnDeriv_ne_zero_imp_of_ae

∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} (ν : MeasureTheory.Measure α)
  [MeasureTheory.SigmaFinite μ] [MeasureTheory.SigmaFinite ν] {p : α → Prop},
  (∀ᵐ (a : α) ∂μ, p a) → ∀ᵐ (a : α) ∂ν, μ.rnDeriv ν a ≠ 0 → p a

Defined in

Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym

Cited by

1 results in Mathlib

Foundations

Depth 217 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.SigmaFiniteMeasureTheory.SigmaFinite