Theorems · Theorem · general topology

MeasurableSet.image_of_monotoneOn

∀ {α : Type u_6} {β : Type u_7} {t : Set α} {g : α → β} [inst : TopologicalSpace α] [inst_1 : MeasurableSpace α]
  [BorelSpace α] [inst_3 : LinearOrder α] [OrderTopology α] [PolishSpace α] [inst : TopologicalSpace β]
  [inst_5 : MeasurableSpace β] [BorelSpace β] [inst_7 : LinearOrder β] [OrderTopology β] [SecondCountableTopology β],
  MeasurableSet t → MonotoneOn g t → MeasurableSet (g '' t)

The image of a measurable set under a monotone map is measurable.

Defined in

Mathlib.MeasureTheory.Constructions.Polish.Basic

Cited by

4 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceMeasurableSpaceBorelSpaceLinearOrderOrderTopologyPolishSpaceTopologicalSpaceMeasurableSpaceBorelSpaceLinearOrderOrderTopologySecondCountableTopology