Theorems · Theorem · measure theory
MeasureTheory.FiniteMeasure.mass_zero_iff
∀ {Ω : Type u_1} [inst : MeasurableSpace Ω] (μ : MeasureTheory.FiniteMeasure Ω), μ.mass = 0 ↔ μ = 0- Cited by
- 5 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
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.
- MeasurableSpacestatement and proof · cited by 13,106
- ENNRealproof · cited by 9,879
- NNRealstatement · cited by 4,310
- MeasureTheory.FiniteMeasurestatement and proof · cited by 150
- MeasureTheory.FiniteMeasure.massstatement and proof · cited by 46
- MeasureTheory.Measure.measure_univ_eq_zeroproof · cited by 26
- ENNReal.coe_eq_zeroproof · cited by 13
- MeasureTheory.FiniteMeasure.ennreal_massproof · cited by 4
- MeasureTheory.FiniteMeasure.toMeasure_injectiveproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- MeasureTheory.FiniteMeasure.mass_nonzero_iffproof · cited by 6
- MeasureTheory.FiniteMeasure.prod_zeroproof · cited by 0
- MeasureTheory.FiniteMeasure.zero_prodproof · cited by 0
- MeasureTheory.FiniteMeasure.restrict_eq_zero_iffproof · cited by 0