Theorems · Theorem · measure theory
MeasureTheory.VectorMeasure.variation_eq_zero
∀ {X : Type u_1} {V : Type u_2} {mX : MeasurableSpace X} [inst : TopologicalSpace V] [inst_1 : ENormedAddCommMonoid V]
[inst_2 : T2Space V] {μ : MeasureTheory.VectorMeasure X V}, μ.variation = 0 ↔ μ = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement · cited by 10,939
- MeasurableSetproof · cited by 3,075
- le_antisymmproof · cited by 2,068
- le_reflproof · cited by 2,061
- T2Spacestatement and proof · cited by 1,351
- le_imp_le_of_le_of_leproof · cited by 576
- MeasureTheory.VectorMeasurestatement and proof · cited by 451
- MeasureTheory.VectorMeasure.variationstatement and proof · cited by 125
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.VectorMeasure.setIntegral_of_variation_apply_eq_zeroproof · cited by 0