Theorems · Theorem · probability

MeasureTheory.Submartingale.pos

∀ {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 : ι → Ω → E},
  MeasureTheory.Submartingale f ℱ μ → MeasureTheory.Submartingale f⁺ ℱ μ

Defined in: Mathlib.Probability.Martingale.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 300 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Preorder NormedAddCommGroup NormedSpace CompleteSpace Lattice ContinuousSup HasSolidNorm IsOrderedAddMonoid IsOrderedModule

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Cites18

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Realstatement and proof · cited by 25,697
NormedAddCommGroupstatement and proof · cited by 15,752
MeasurableSpacestatement and proof · cited by 13,106
NormedSpacestatement and proof · cited by 12,499
MeasureTheory.Measurestatement and proof · cited by 10,939
Preorderstatement and proof · cited by 7,952
CompleteSpacestatement and proof · cited by 2,532
IsOrderedAddMonoidstatement and proof · cited by 1,659
Latticestatement and proof · cited by 916
MeasureTheory.Filtrationstatement and proof · cited by 425
IsOrderedModulestatement and proof · cited by 156
PosPart.posPartstatement · cited by 113

Cited by2

Results whose statement or proof uses this declaration.

MeasureTheory.Submartingale.mul_lintegral_upcrossings_le_lintegral_pos_partproof · cited by 1
MeasureTheory.mul_integral_upcrossingsBefore_le_integral_pos_part_auxproof · cited by 1