Theorems · Theorem · measure theory
MeasureTheory.VectorMeasure.semivariation_apply_le_bound
∀ {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 : Set X}, μ.semivariation s ≤ ↑μ.bound- Cited by
- 1 results in Mathlib
- Foundations
- Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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 and proof · cited by 9,879
- Set.univproof · cited by 3,945
- ENNReal.ofNNRealstatement · cited by 1,279
- LT.lt.neproof · cited by 872
- MeasureTheory.VectorMeasurestatement and proof · cited by 451
- LE.le.trans_eqproof · cited by 328
- Set.subset_univproof · cited by 228
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.VectorMeasure.enorm_apply_le_boundproof · cited by 1