Theorems · Theorem · measure theory

Continuous.measurable

∀ {α : Type u_1} {γ : Type u_3} [inst : TopologicalSpace α] [inst_1 : MeasurableSpace α] [OpensMeasurableSpace α]
  [inst_3 : TopologicalSpace γ] [inst_4 : MeasurableSpace γ] [BorelSpace γ] {f : α → γ}, Continuous f → Measurable f

A continuous function from an OpensMeasurableSpace to a BorelSpace is measurable.

Defined in

Mathlib.MeasureTheory.Constructions.BorelSpace.Basic

Cited by

181 results in Mathlib

Foundations

Depth 64 from the axioms, rests on 725 definitions · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceMeasurableSpaceOpensMeasurableSpaceTopologicalSpaceMeasurableSpaceBorelSpace