Theorems · Theorem · measure theory
MeasureTheory.Measure.exists_isOpen_measure_lt_top
∀ {α : Type u_1} {m0 : MeasurableSpace α} [inst : TopologicalSpace α] (μ : MeasureTheory.Measure α)
[MeasureTheory.IsLocallyFiniteMeasure μ] (x : α), ∃ s, x ∈ s ∧ IsOpen s ∧ μ s < ⊤- Cited by
- 4 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- IsOpenstatement · cited by 2,400
- MeasureTheory.IsLocallyFiniteMeasurestatement and proof · cited by 171
- nhds_basis_opensproof · cited by 54
- MeasureTheory.Measure.finiteAt_nhdsproof · cited by 10
- MeasureTheory.Measure.FiniteAtFilter.exists_mem_basisproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- VitaliFamily.measure_limRatioMeas_topproof · cited by 2
- VitaliFamily.null_of_frequently_le_of_frequently_geproof · cited by 1
- VitaliFamily.measure_limRatioMeas_zeroproof · cited by 1
- MeasureTheory.Measure.isTopologicalBasis_isOpen_lt_topproof · cited by 0