Theorems · Definition · measure theory
MeasureTheory.Measure.real
{α : Type u_6} → {m : MeasurableSpace α} → MeasureTheory.Measure α → Set α → ℝThe real-valued version of a measure. Maps infinite measure sets to zero. Use as μ.real s.
The API is developed in Mathlib/MeasureTheory/Measure/Real.lean.
- Cited by
- 530 results in Mathlib
- Foundations
- Depth 170 from the axioms, rests on 4,584 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Realstatement · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNReal.toRealproof · cited by 859
Cited by541
Results whose statement or proof uses this declaration.
- MeasureTheory.DominatedFinMeasAdditiveproof · cited by 138
- MeasureTheory.integral_conststatement and proof · cited by 75
- MeasureTheory.measureReal_defstatement · cited by 68
- MeasureTheory.probReal_univstatement · cited by 39
- MeasureTheory.Measure.toSignedMeasureproof · cited by 36
- MeasureTheory.dominatedFinMeasAdditive_weightedSMulproof · cited by 35
- MeasureTheory.weightedSMulproof · cited by 31
- MeasureTheory.measureReal_restrict_applystatement · cited by 29
- MeasureTheory.Measure.toBoxAdditiveproof · cited by 22
- MeasureTheory.measureReal_nonnegstatement · cited by 21
- MeasureTheory.setIntegral_conststatement and proof · cited by 15
- MeasureTheory.dominatedFinMeasAdditive_condExpIndproof · cited by 14
Showing the 200 most cited of 541.