Theorems · Theorem · probability

MeasureTheory.Submartingale.sup

∀ {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 : MeasureTheory.Filtration ι m0} [CompleteSpace E] [inst_4 : Lattice E] [ContinuousSup E] [HasSolidNorm E]
  [IsOrderedAddMonoid E] [IsOrderedModule ℝ E] {f g : ι → Ω → E},
  MeasureTheory.Submartingale f ℱ μ → MeasureTheory.Submartingale g ℱ μ → MeasureTheory.Submartingale (f ⊔ g) ℱ μ

Defined in

Mathlib.Probability.Martingale.Basic

Cited by

1 results in Mathlib

Foundations

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

Assumes

PreorderNormedAddCommGroupNormedSpaceCompleteSpaceLatticeContinuousSupHasSolidNormIsOrderedAddMonoidIsOrderedModule