Theorems · Theorem · probability
ProbabilityTheory.IsAEKolmogorovProcess.kolmogorovCondition
∀ {T : Type u_1} {Ω : Type u_2} {E : Type u_3} [inst : PseudoEMetricSpace T] {mΩ : MeasurableSpace Ω}
[inst_1 : PseudoEMetricSpace E] {p q : ℝ} {M : NNReal} {P : MeasureTheory.Measure Ω} {X : T → Ω → E},
ProbabilityTheory.IsAEKolmogorovProcess X P p q M →
∀ (s t : T), ∫⁻ (ω : Ω), edist (X s ω) (X t ω) ^ p ∂P ≤ ↑M * edist s t ^ q- Defined in
- Mathlib.Probability.Process.Kolmogorov
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- NNRealstatement and proof · cited by 4,310
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.ofNNRealstatement and proof · cited by 1,279
- MeasureTheory.lintegralstatement and proof · cited by 1,152
- EDist.ediststatement and proof · cited by 735
- MeasureTheory.lintegral_congr_aeproof · cited by 95
Cited by2
Results whose statement or proof uses this declaration.
- ProbabilityTheory.IsAEKolmogorovProcess.edist_eq_zeroproof · cited by 1
- ProbabilityTheory.IsAEKolmogorovProcess.edist_eq_zero_of_const_eq_zeroproof · cited by 1