Theorems · Theorem · functional analysis

MeasureTheory.L1.ofReal_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)), ENNReal.ofReal ‖f - g‖ = ∫⁻ (x : α), ‖↑↑f x - ↑↑g x‖ₑ ∂μ

Computing the norm of a difference between two L¹-functions. Note that this is not a special case of ofReal_norm_eq_lintegral 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 226 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroup