Theorems · Theorem · measure theory
MeasureTheory.Measure.Regular.exists_isCompact_not_null
∀ {α : Type u_1} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} [inst_1 : TopologicalSpace α] [μ.Regular],
(∃ K, IsCompact K ∧ μ K ≠ 0) ↔ μ ≠ 0- Defined in
- Mathlib.MeasureTheory.Measure.Regular
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · 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
- Set.univproof · cited by 3,945
- IsCompactstatement and proof · cited by 1,282
- isOpen_univproof · cited by 112
- MeasureTheory.Measure.Regularstatement and proof · cited by 61
- IsOpen.measure_eq_iSup_isCompactproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.measure_isOpen_pos_of_smulInvariant_of_ne_zeroproof · cited by 1
- MeasureTheory.measure_isOpen_pos_of_vaddInvariant_of_ne_zeroproof · cited by 1