Theorems · Theorem · measure theory
IsCompact.measure_lt_top
∀ {α : Type u_1} {m0 : MeasurableSpace α} [inst : TopologicalSpace α] {μ : MeasureTheory.Measure α}
[MeasureTheory.IsFiniteMeasureOnCompacts μ] ⦃K : Set α⦄, IsCompact K → μ K < ⊤A compact subset has finite measure for a measure which is finite on compacts.
- Cited by
- 35 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Top.topstatement · cited by 9,680
- IsCompactstatement and proof · cited by 1,282
- MeasureTheory.IsFiniteMeasureOnCompactsstatement and proof · cited by 109
- MeasureTheory.IsFiniteMeasureOnCompacts.lt_top_of_isCompactproof · cited by 3
Cited by35
Results whose statement or proof uses this declaration.
- IsCompact.measure_ne_topproof · cited by 12
- Bornology.IsBounded.measure_lt_topproof · cited by 8
- measure_Icc_lt_topproof · cited by 5
- MeasureTheory.Measure.isAddLeftInvariant_eq_smul_of_regularproof · cited by 4
- MeasureTheory.Measure.isMulLeftInvariant_eq_smul_of_regularproof · cited by 3
- MeasureTheory.eventually_nhds_one_measure_smul_sdiff_ltproof · cited by 3
- MonotoneOn.memLp_isCompactproof · cited by 3
- IsCompact.exists_isOpen_lt_addproof · cited by 3
- MeasureTheory.Measure.isMulLeftInvariant_eq_smul_of_innerRegularproof · cited by 2
- MeasureTheory.eventually_nhds_zero_measure_vadd_sdiff_ltproof · cited by 2
- BoxIntegral.Box.measure_Icc_lt_topproof · cited by 2