Theorems · Theorem · measure theory

MeasureTheory.L1.SimpleFunc.setToL1S_mono_left

∀ {α : Type u_1} {E : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {m : MeasurableSpace α}
  {μ : MeasureTheory.Measure α} {G'' : Type u_7} [inst_2 : NormedAddCommGroup G''] [inst_3 : PartialOrder G'']
  [IsOrderedAddMonoid G''] [inst_5 : NormedSpace ℝ G''] {T T' : Set α → E →L[ℝ] G''},
  (∀ (s : Set α) (x : E), (T s) x ≤ (T' s) x) →
    ∀ (f : ↥(α →₁ₛ[μ] E)), MeasureTheory.L1.SimpleFunc.setToL1S T f ≤ MeasureTheory.L1.SimpleFunc.setToL1S T' f

Defined in

Mathlib.MeasureTheory.Integral.SetToL1

Cited by

0 results in Mathlib

Foundations

Depth 226 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupPartialOrderIsOrderedAddMonoidNormedSpace