Theorems · Theorem · measure theory
MeasureTheory.isFiniteMeasure_withDensity
∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ENNReal},
∫⁻ (a : α), f a ∂μ ≠ ⊤ → MeasureTheory.IsFiniteMeasure (μ.withDensity f)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- MeasureTheory.lintegralstatement and proof · cited by 1,152
- MeasureTheory.IsFiniteMeasurestatement · cited by 1,078
- MeasureTheory.Measure.withDensitystatement · cited by 265
- MeasurableSet.univproof · cited by 178
- lt_top_iff_ne_topproof · cited by 95
- MeasureTheory.Measure.restrict_univproof · cited by 76
- MeasureTheory.withDensity_applyproof · cited by 73
Cited by3
Results whose statement or proof uses this declaration.
- VitaliFamily.ae_tendsto_lintegral_div'proof · cited by 2
- MeasureTheory.isFiniteMeasure_withDensity_ofRealproof · cited by 2
- MeasureTheory.withDensityᵥ_toRealstatement and proof · cited by 1