Theorems · Theorem · number theory

AbstractMeasure.prodMk_prod_apply

∀ {X : Type u_1} {Y : Type u_2} {R : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  [inst_2 : CommRing R] [inst_3 : TopologicalSpace R] [inst_4 : IsTopologicalRing R] (μ : AbstractMeasure X R R)
  (ν : AbstractMeasure Y R R) [inst_5 : LocallyCompactSpace X] [inst_6 : LocallyCompactSpace Y] (f : C(X, R))
  (g : C(Y, R)), ((AbstractMeasure.prodMk μ) ν) (f.comp ContinuousMap.fst * g.comp ContinuousMap.snd) = μ f * ν g

On functions of the form (x, y) ↦ f x * g y, the measure prodMk μ ν agrees with the algebraic tensor product of μ and ν.

Defined in

Mathlib.NumberTheory.Padics.Measure.Basic

Cited by

1 results in Mathlib

Foundations

Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceCommRingTopologicalSpaceIsTopologicalRingLocallyCompactSpaceLocallyCompactSpace