Theorems · Theorem · functional analysis

MeasureTheory.L1.norm_sub_eq_lintegral

∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup β]
  (f g : ↥(MeasureTheory.Lp β 1 μ)), ‖f - g‖ = (∫⁻ (x : α), ‖↑↑f x - ↑↑g x‖ₑ ∂μ).toReal

Computing the norm of a difference between two L¹-functions. Note that this is not a special case of norm_def since (f - g) x and f x - g x are not equal (but only a.e.-equal).

Defined in

Mathlib.MeasureTheory.Function.L1Space.AEEqFun

Cited by

0 results in Mathlib

Foundations

Depth 223 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroup