Theorems · Theorem · measure theory

intervalIntegral.norm_integral_le_abs_integral_norm

∀ {E : Type u_5} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {a b : ℝ} {f : ℝ → E}
  {μ : MeasureTheory.Measure ℝ}, ‖∫ (x : ℝ) in a..b, f x ∂μ‖ ≤ |∫ (x : ℝ) in a..b, ‖f x‖ ∂μ|

Defined in

Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic

Cited by

0 results in Mathlib

Foundations

Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace