Theorems · Theorem · measure theory

MeasureTheory.IsLocallyFiniteMeasure.withDensity_ofReal

∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : TopologicalSpace α]
  [OpensMeasurableSpace α] [MeasureTheory.IsLocallyFiniteMeasure μ] {f : α → ℝ},
  Continuous f → MeasureTheory.IsLocallyFiniteMeasure (μ.withDensity fun x => ENNReal.ofReal (f x))

Defined in

Mathlib.MeasureTheory.Measure.WithDensity

Cited by

0 results in Mathlib

Foundations

Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceOpensMeasurableSpaceMeasureTheory.IsLocallyFiniteMeasure