Theorems · Theorem · measure theory
MeasureTheory.Measure.absolutelyContinuous_zero_iff
∀ {α : Type u_1} {mα : MeasurableSpace α} {μ : MeasureTheory.Measure α}, μ.AbsolutelyContinuous 0 ↔ μ = 0- Cited by
- 3 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Set.univproof · cited by 3,945
- MeasureTheory.Measure.AbsolutelyContinuousstatement and proof · cited by 325
- MeasureTheory.Measure.measure_univ_eq_zeroproof · cited by 26
- MeasureTheory.Measure.AbsolutelyContinuous.zeroproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- InformationTheory.klDiv_zero_rightproof · cited by 1
- InformationTheory.mul_log_le_toReal_klDivproof · cited by 1
- InformationTheory.integral_llr_add_mul_log_nonnegproof · cited by 0