Theorems · Theorem · measure theory

MeasureTheory.SimpleFunc.setToSimpleFunc_mono_left

∀ {α : Type u_1} {F : Type u_3} [inst : NormedAddCommGroup F] [inst_1 : NormedSpace ℝ F] {G'' : Type u_8}
  [inst_2 : NormedAddCommGroup G''] [inst_3 : PartialOrder G''] [IsOrderedAddMonoid G''] [inst_5 : NormedSpace ℝ G'']
  {m : MeasurableSpace α} (T T' : Set α → F →L[ℝ] G''),
  (∀ (s : Set α) (x : F), (T s) x ≤ (T' s) x) →
    ∀ (f : MeasureTheory.SimpleFunc α F),
      MeasureTheory.SimpleFunc.setToSimpleFunc T f ≤ MeasureTheory.SimpleFunc.setToSimpleFunc T' f

Defined in

Mathlib.MeasureTheory.Integral.FinMeasAdditive

Cited by

2 results in Mathlib

Foundations

Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupPartialOrderIsOrderedAddMonoidNormedSpace