Theorems · Theorem · probability

MeasureTheory.Supermartingale.smul_nonneg

∀ {Ω : Type u_1} {ι : Type u_3} [inst : Preorder ι] {m0 : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω}
  {ℱ : MeasureTheory.Filtration ι m0} {F : Type u_4} [inst_1 : NormedAddCommGroup F] [inst_2 : PartialOrder F]
  [inst_3 : NormedSpace ℝ F] [CompleteSpace F] [IsOrderedModule ℝ F] {f : ι → Ω → F} {c : ℝ},
  0 ≤ c → MeasureTheory.Supermartingale f ℱ μ → MeasureTheory.Supermartingale (c • f) ℱ μ

Defined in

Mathlib.Probability.Martingale.Basic

Cited by

2 results in Mathlib

Foundations

Depth 298 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderNormedAddCommGroupPartialOrderNormedSpaceCompleteSpaceIsOrderedModule