Theorems · Theorem · measure theory

MeasureTheory.L1.SimpleFunc.norm_eq_sum_mul

∀ {α : Type u_1} {G : Type u_5} [inst : NormedAddCommGroup G] {m : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  (f : ↥(α →₁ₛ[μ] G)),
  ‖f‖ =
    ∑ x ∈ (MeasureTheory.Lp.simpleFunc.toSimpleFunc f).range,
      μ.real (⇑(MeasureTheory.Lp.simpleFunc.toSimpleFunc f) ⁻¹' {x}) * ‖x‖

Defined in

Mathlib.MeasureTheory.Integral.SetToL1

Cited by

2 results in Mathlib

Foundations

Depth 233 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroup