Theorems · Theorem · measure theory
MeasureTheory.SigmaFinite.withDensity_of_ne_top
∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [MeasureTheory.SigmaFinite μ] {f : α → ENNReal},
(∀ᵐ (x : α) ∂μ, f x ≠ ⊤) → MeasureTheory.SigmaFinite (μ.withDensity f)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasureTheory.SigmaFinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Top.topstatement and proof · cited by 9,680
- Filter.Eventuallystatement and proof · cited by 3,134
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.EventuallyEqproof · cited by 1,912
- ENNReal.ofNNRealproof · cited by 1,279
- Filter.Eventually.monoproof · cited by 646
- MeasureTheory.SigmaFinitestatement and proof · cited by 526
- MeasureTheory.Measure.withDensitystatement · cited by 265
- ENNReal.toNNRealproof · cited by 165
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.rnDeriv_withDensity_withDensity_rnDeriv_leftproof · cited by 1
- MeasureTheory.Measure.rnDeriv_withDensity_withDensity_rnDeriv_rightproof · cited by 1
- MeasureTheory.Measure.rnDeriv_withDensity_right_of_absolutelyContinuousproof · cited by 1
- MeasureTheory.SigmaFinite.withDensity_of_ne_top'proof · cited by 0