Theorems · Theorem · measure theory

intervalIntegral.norm_integral_le_of_norm_le_const_ae

∀ {E : Type u_5} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {a b C : ℝ} {f : ℝ → E},
  (∀ᵐ (x : ℝ), x ∈ Set.uIoc a b → ‖f x‖ ≤ C) → ‖∫ (x : ℝ) in a..b, f x‖ ≤ C * |b - a|

Defined in

Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic

Cited by

1 results in Mathlib

Foundations

Depth 259 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace