Theorems · Theorem · real analysis
MonotoneOn.eVariationOn_le
Deprecated since 2026-07-08Use MonotoneOn.eVariationOn_eq instead.
∀ {α : Type u_1} [inst : LinearOrder α] {f : α → ℝ} {s : Set α} {a b : α},
MonotoneOn f s → a ∈ s → b ∈ s → eVariationOn f (s ∩ Set.Icc a b) ≤ ENNReal.ofReal (f b - f a)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrder
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Cites10
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
- ENNRealstatement · cited by 9,879
- LinearOrderstatement and proof · cited by 8,572
- Set.Iccstatement · cited by 1,702
- ENNReal.ofRealstatement · cited by 863
- Eq.leproof · cited by 605
- MonotoneOnstatement and proof · cited by 311
- eVariationOnstatement · cited by 90
- MonotoneOn.eVariationOn_eqproof · cited by 4
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