Theorems · Theorem · probability

MeasureTheory.Submartingale.neg

∀ {Ω : Type u_1} {E : Type u_2} {ι : Type u_3} [inst : Preorder ι] {m0 : MeasurableSpace Ω}
  {μ : MeasureTheory.Measure Ω} [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace ℝ E] {f : ι → Ω → E}
  {ℱ : MeasureTheory.Filtration ι m0} [CompleteSpace E] [inst_4 : Preorder E] [AddLeftMono E],
  MeasureTheory.Submartingale f ℱ μ → MeasureTheory.Supermartingale (-f) ℱ μ

Defined in

Mathlib.Probability.Martingale.Basic

Cited by

7 results in Mathlib

Foundations

Depth 299 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreorderNormedAddCommGroupNormedSpaceCompleteSpacePreorderAddLeftMono