Theorems · Theorem · measure theory
MeasureTheory.VectorMeasure.semivariation_mono
∀ {X : Type u_1} {E : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {mX : MeasurableSpace X}
{μ : MeasureTheory.VectorMeasure X E} {s t : Set X}, s ⊆ t → μ.semivariation s ≤ μ.semivariation t- Cited by
- 2 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.
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
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- MeasurableSpacestatement and proof · cited by 13,106
- NormedSpacestatement and proof · cited by 12,499
- ENNRealstatement · cited by 9,879
- Set.ofPredproof · cited by 6,101
- LE.le.transproof · cited by 3,151
- ENorm.enormproof · cited by 715
- StrongDualproof · cited by 459
- MeasureTheory.VectorMeasurestatement and proof · cited by 451
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.VectorMeasure.semivariation_apply_le_boundproof · cited by 1
- MeasureTheory.VectorMeasure.enorm_apply_le_semivariation_of_subsetproof · cited by 0