mul — Mathlib

English

If u and v are adapted with respect to a filtration f, and β has a division operation with a continuous division, then u/v is adapted with respect to the same filtration.

Русский

Если u и v адаптированы относительно фильтрации и есть непрерывное деление, то u/v также адаптировано по той же фильтрации.

LaTeX

$$$$ \\forall i, \\ (hu(i)) \\div (hv(i)) \\in \\text{Adapted}(f, u/v) $$$$

Lean4

@[to_additive]
protected theorem mul [Mul β] [ContinuousMul β] (hu : Adapted f u) (hv : Adapted f v) : Adapted f (u * v) := fun i =>
  (hu i).mul (hv i)

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