Theorems · Theorem · real analysis

eVariationOn_fun_mul_le

∀ {α : Type u_2} [inst : LinearOrder α] {f g : α → ℝ} {C D : ENNReal} {s : Set α},
  (∀ x ∈ s, ‖f x‖ₑ ≤ C) →
    (∀ x ∈ s, ‖g x‖ₑ ≤ D) → eVariationOn (fun i => f i * g i) s ≤ C * eVariationOn g s + D * eVariationOn f s

Eta-expanded form of eVariation_mul_le

Defined in: Mathlib.Analysis.BoundedVariation
Cited by: 0 results in Mathlib
Foundations: Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: LinearOrder

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Setstatement · cited by 53,352
Realstatement · cited by 25,697
ENNRealstatement · cited by 9,879
LinearOrderstatement · cited by 8,572
ENorm.enormstatement · cited by 715
eVariationOnstatement · cited by 90
eVariation_mul_leproof · cited by 1

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