Theorems · Theorem · probability
ProbabilityTheory.IsPreBrownianReal.smul
∀ {Ω : Type u_1} {mΩ : MeasurableSpace Ω} {B : NNReal → Ω → ℝ} {P : MeasureTheory.Measure Ω},
ProbabilityTheory.IsPreBrownianReal B P →
∀ {c : NNReal}, c ≠ 0 → ProbabilityTheory.IsPreBrownianReal (fun t ω => (√↑c)⁻¹ * B (c * t) ω) PIf B is a pre-Brownian motion and c > 0, then
t ↦ (√c)⁻¹ B (c t) is a pre-Brownian motion.
- Defined in
- Mathlib.Probability.BrownianMotion.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 324 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
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
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- MulZeroClass.mul_zeroproof · cited by 2,091
- NNReal.toRealstatement and proof · cited by 1,260
- one_ne_zeroproof · cited by 885
- ne_of_gtproof · cited by 637
- div_oneproof · cited by 629
- Real.sqrtstatement and proof · cited by 545
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.IsBrownianReal.smulproof · cited by 0