Theorems · Theorem · measure theory
MeasureTheory.ae_withDensity_iff
∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {p : α → Prop} {f : α → ENNReal},
Measurable f → ((∀ᵐ (x : α) ∂μ.withDensity f, p x) ↔ ∀ᵐ (x : α) ∂μ, f x ≠ 0 → p x)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Filter.Eventuallystatement · cited by 3,134
- MeasureTheory.aestatement · cited by 2,352
- Measurablestatement and proof · cited by 1,499
- Measurable.aemeasurableproof · cited by 304
- MeasureTheory.Measure.withDensitystatement · cited by 265
- MeasureTheory.ae_withDensity_iff'proof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.rnDeriv_posproof · cited by 9
- integral_withDensity_eq_integral_smulproof · cited by 4
- aestronglyMeasurable_withDensity_iffproof · cited by 1
- aemeasurable_withDensity_iffproof · cited by 0