Theorems · Theorem · measure theory

MeasureTheory.ProbabilityMeasure.continuous_pi

∀ {ι : Type u_1} {α : ι → Type u_2} [inst : Fintype ι] [inst_1 : (i : ι) → MeasurableSpace (α i)]
  [inst_2 : (i : ι) → TopologicalSpace (α i)] [inst_3 : ∀ (i : ι), SecondCountableTopology (α i)]
  [∀ (i : ι), TopologicalSpace.PseudoMetrizableSpace (α i)] [inst_5 : ∀ (i : ι), OpensMeasurableSpace (α i)],
  Continuous fun μ => MeasureTheory.ProbabilityMeasure.pi μ

The map associating to finitely many probability measures their product is a continuous map.

Defined in

Mathlib.MeasureTheory.Measure.FiniteMeasurePi

Cited by

0 results in Mathlib

Foundations

Depth 271 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeMeasurableSpaceTopologicalSpaceSecondCountableTopologyTopologicalSpace.PseudoMetrizableSpaceOpensMeasurableSpace