Theorems · Theorem · probability
ProbabilityTheory.IsPreBrownianReal.covariance_eval
∀ {Ω : Type u_1} {mΩ : MeasurableSpace Ω} {B : NNReal → Ω → ℝ} {P : MeasureTheory.Measure Ω},
ProbabilityTheory.IsPreBrownianReal B P → ∀ (s t : NNReal), ProbabilityTheory.covariance (B s) (B t) P = ↑(min s t)- Defined in
- Mathlib.Probability.BrownianMotion.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 320 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- NNRealstatement and proof · cited by 4,310
- NNReal.toRealstatement and proof · cited by 1,260
- Measurable.aemeasurableproof · cited by 304
- Function.evalproof · cited by 140
- ProbabilityTheory.covariancestatement and proof · cited by 96
- measurable_pi_applyproof · cited by 77
- Finset.restrictproof · cited by 60
- ProbabilityTheory.IsPreBrownianRealstatement and proof · cited by 23
- ProbabilityTheory.BrownianReal.projectiveFamilyproof · cited by 19
Cited by5
Results whose statement or proof uses this declaration.
- ProbabilityTheory.IsPreBrownianReal.smulproof · cited by 1
- ProbabilityTheory.IsPreBrownianReal.covariance_fun_evalproof · cited by 1
- ProbabilityTheory.IsPreBrownianReal.shiftproof · cited by 1
- ProbabilityTheory.IsPreBrownianReal.indepFun_shiftproof · cited by 0
- ProbabilityTheory.IsPreBrownianReal.invproof · cited by 0