Theorems · Theorem · measure theory
Bornology.IsBounded.measure_lt_top
∀ {α : Type u_1} {m0 : MeasurableSpace α} [inst : PseudoMetricSpace α] [ProperSpace α] {μ : MeasureTheory.Measure α}
[MeasureTheory.IsFiniteMeasureOnCompacts μ] ⦃s : Set α⦄, Bornology.IsBounded s → μ s < ⊤A bounded subset has finite measure for a measure which is finite on compact sets, in a proper space.
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- 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
- PseudoMetricSpacestatement and proof · cited by 1,550
- MeasureTheory.measure_monoproof · cited by 338
- subset_closureproof · cited by 309
- Bornology.IsBoundedstatement and proof · cited by 293
- isClosed_closureproof · cited by 195
- ProperSpacestatement and proof · cited by 190
Cited by8
Results whose statement or proof uses this declaration.
- MeasureTheory.measure_closedBall_lt_topproof · cited by 6
- NumberField.mixedEmbedding.minkowskiBound_lt_topproof · cited by 2
- tendsto_measure_cthickening_of_isCompactproof · cited by 1
- ZLattice.covolume_ne_zeroproof · cited by 1
- MeasureTheory.Measure.addHaar_eq_zero_of_disjoint_translates_auxproof · cited by 1
- MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_leproof · cited by 1
- Convex.addHaar_frontierproof · cited by 1
- MeasureTheory.measure_ball_ne_topproof · cited by 1