Theorems · Theorem · measure theory
MeasureTheory.isFiniteMeasure_withDensity_ofReal
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ℝ},
MeasureTheory.HasFiniteIntegral f μ → MeasureTheory.IsFiniteMeasure (μ.withDensity fun x => ENNReal.ofReal (f x))- Cited by
- 2 results in Mathlib
- Foundations
- Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.IsFiniteMeasurestatement · cited by 1,078
- LT.lt.neproof · cited by 872
- ENNReal.ofRealstatement · cited by 863
- LE.le.trans_ltproof · cited by 795
- MeasureTheory.Measure.withDensitystatement · cited by 265
- MeasureTheory.HasFiniteIntegralstatement and proof · cited by 120
- MeasureTheory.lintegral_monoproof · cited by 51
- MeasureTheory.isFiniteMeasure_withDensityproof · cited by 3
- Real.ofReal_le_enormproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.withDensityᵥ_eq_withDensity_pos_part_sub_withDensity_neg_partstatement and proof · cited by 1