Theorems · Inductive type · measure theory
MeasureTheory.IsFiniteMeasureOnCompacts
{α : Type u_1} → {m0 : MeasurableSpace α} → [TopologicalSpace α] → MeasureTheory.Measure α → PropA measure μ is finite on compacts if any compact set K satisfies μ K < ∞.
- Cited by
- 109 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 4 definitions · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
- MeasurableSpacestatement · cited by 13,106
- MeasureTheory.Measurestatement · cited by 10,939
Cited by121
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.addHaarScalarFactorstatement and proof · cited by 58
- IsCompact.measure_lt_topstatement and proof · cited by 35
- MeasureTheory.Measure.haarScalarFactorstatement and proof · cited by 31
- Continuous.integrable_of_hasCompactSupportstatement and proof · cited by 18
- IsCompact.measure_ne_topstatement and proof · cited by 12
- Continuous.integral_pos_of_hasCompactSupport_nonneg_nonzerostatement and proof · cited by 11
- MeasureTheory.Measure.Regular.mapproof · cited by 9
- CompactlySupportedContinuousMap.integrablestatement and proof · cited by 9
- ContinuousOn.integrableOn_Iccstatement and proof · cited by 8
- ContinuousOn.integrableOn_compactstatement and proof · cited by 8
- Bornology.IsBounded.measure_lt_topstatement and proof · cited by 8
- MeasureTheory.Measure.isAddLeftInvariant_eq_smulstatement and proof · cited by 8