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Theorems · Theorem · real analysis

eVariation_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 (f * g) s ≤ C * eVariationOn g s + D * eVariationOn f s
Defined in
Mathlib.Analysis.BoundedVariation
Cited by
1 results in Mathlib
Foundations
Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrder
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

eVariationOn_fun_mul_le · cited by 0eVariationOn_fun_mul_leSet · cited by 53352SetReal · cited by 25697RealENNReal · cited by 9879ENNRealLinearOrder · cited by 8572LinearOrderENorm.enorm · cited by 715ENorm.enormeVariationOn · cited by 90eVariationOneVariationOn_smul_le · cited by 2eVariationOn_smul_leeVariation_mul_leCITED BYCITES

Cites7

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Cited by1

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