Theorems · Theorem · measure theory
MeasureTheory.Measure.zero_one
∀ {α : Type u_1} {mα : MeasurableSpace α} (μ : MeasureTheory.Measure α) [MeasureTheory.IsZeroOneMeasure μ] (s : Set α),
μ s = 0 ∨ μ s = 1- Cited by
- 5 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- MeasurableSetproof · cited by 3,075
- MeasureTheory.exists_measurable_supersetproof · cited by 10
- MeasureTheory.IsZeroOneMeasurestatement and proof · cited by 8
- MeasureTheory.IsZeroOneMeasure.zero_one₀proof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- MeasureTheory.IsZeroOneMeasure.measure_inter_eq_oneproof · cited by 1
- MeasureTheory.IsZeroOneMeasure.measure_inter_eq_prodproof · cited by 1
- MeasureTheory.IsZeroOneMeasure.exists_eq_diracproof · cited by 1
- ProbabilityTheory.Kernel.comp_parallelComp_comp_copyproof · cited by 0