instPseudoEMetricSpace — Mathlib

English

There is a natural emetric space structure on the finite product PiLp p β, compatible with the product uniformity.

Русский

Существует естественная структура псевдометрического пространства на конечном произведении PiLp p β, согласованная с произведением равномерностей.

LaTeX

$$EMetricSpace (PiLp p β)$$

Lean4

/-- pseudoemetric space instance on the product of finitely many pseudoemetric spaces, using the
`L^p` pseudoedistance, and having as uniformity the product uniformity. -/
instance [∀ i, PseudoEMetricSpace (β i)] : PseudoEMetricSpace (PiLp p β) :=
  (pseudoEmetricAux p β).replaceUniformity (uniformity_aux p β).symm

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