Theorems · Theorem · real analysis

enorm_sub_le_lintegral_derivWithin_Icc_of_contDiffOn_Icc

∀ {E : Type u_3} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f : ℝ → E} {a b : ℝ},
  ContDiffOn ℝ 1 f (Set.Icc a b) → a ≤ b → ‖f b - f a‖ₑ ≤ ∫⁻ (x : ℝ) in Set.Icc a b, ‖derivWithin f (Set.Icc a b) x‖ₑ

Defined in

Mathlib.MeasureTheory.Integral.IntervalIntegral.ContDiff

Cited by

1 results in Mathlib

Foundations

Depth 269 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace