Theorems · Theorem · measure theory
MeasureTheory.preVariation.exists_Finpartition_sum_ge
∀ {X : Type u_1} [inst : MeasurableSpace X] (f : Set X → ENNReal) {s : Set X} (hs : MeasurableSet s) {ε : NNReal},
0 < ε → MeasureTheory.preVariationFun f s ≠ ⊤ → ∃ P, MeasureTheory.preVariationFun f s ≤ ∑ p ∈ P.parts, f ↑p + ↑ε- Cited by
- 2 results in Mathlib
- Foundations
- Depth 129 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.
Cites25
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
- MeasurableSpacestatement and proof · cited by 13,106
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- Finset.sumstatement and proof · cited by 5,195
- NNRealstatement and proof · cited by 4,310
- MeasurableSetstatement and proof · cited by 3,075
- le_reflproof · cited by 2,061
- ENNReal.ofNNRealstatement and proof · cited by 1,279
- le_of_ltproof · cited by 1,175
- add_le_addproof · cited by 666
- ne_of_gtproof · cited by 637
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.preVariation.sum_le_preVariationFun_iUnionproof · cited by 1
- MeasureTheory.preVariation.exists_Finpartition_sum_ge'proof · cited by 1