Theorems · Theorem · measure theory

MeasureTheory.SimpleFunc.norm_approxOn_zero_le

∀ {β : Type u_2} {E : Type u_4} [inst : MeasurableSpace β] [inst_1 : MeasurableSpace E] [inst_2 : NormedAddCommGroup E]
  [inst_3 : OpensMeasurableSpace E] {f : β → E} (hf : Measurable f) {s : Set E} (h₀ : 0 ∈ s)
  [inst_4 : TopologicalSpace.SeparableSpace ↑s] (x : β) (n : ℕ),
  ‖(MeasureTheory.SimpleFunc.approxOn f hf s 0 h₀ n) x‖ ≤ ‖f x‖ + ‖f x‖

Defined in

Mathlib.MeasureTheory.Function.SimpleFuncDenseLp

Cited by

2 results in Mathlib

Foundations

Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpaceNormedAddCommGroupOpensMeasurableSpaceTopologicalSpace.SeparableSpace