pi' — Mathlib

English

The equality pi'_pi holds for encodable index with SigmaFinite μ i, giving the same product formula as pi'_pi.

Русский

Уравнение pi'_pi выполняется для кодируемого индекса и сигма-ограниченных μ_i, причем формула совпадает с произведением.

LaTeX

$$pi' μ evaluated on universal product equals ∏ i μ_i(s_i)$$

Lean4

/-- The product measure on an encodable finite type, defined by mapping `Measure.tprod` along the
  equivalence `MeasurableEquiv.piMeasurableEquivTProd`.
  The definition `MeasureTheory.Measure.pi` should be used instead of this one. -/
def pi' : Measure (∀ i, α i) :=
  Measure.map (TProd.elim' mem_sortedUniv) (Measure.tprod (sortedUniv ι) μ)

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