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Theorems · Theorem · general topology

Continuous.map_eq_borel

∀ {X : Type u_3} {Y : Type u_4} [inst : TopologicalSpace X] [PolishSpace X] [inst_2 : MeasurableSpace X] [BorelSpace X]
  [inst_4 : TopologicalSpace Y] [T0Space Y] [SecondCountableTopology Y] {f : X → Y},
  Continuous f → Function.Surjective f → MeasurableSpace.map f inst_2 = borel Y
Defined in
Mathlib.MeasureTheory.Constructions.Polish.Basic
Cited by
1 results in Mathlib
Foundations
Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpacePolishSpaceMeasurableSpaceBorelSpaceTopologicalSpaceT0SpaceSecondCountableTopology
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Continuous.map_borel_eq · cited by 0Continuous.map_borel_eqTopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceContinuous · cited by 2592ContinuousBorelSpace · cited by 1602BorelSpaceSecondCountableTopology · cited by 750SecondCountableTopologyContinuous.measurable · cited by 181Continuous.measurableT0Space · cited by 179T0Spaceborel · cited by 57borelPolishSpace · cited by 57PolishSpaceMeasurableSpace.map · cited by 23MeasurableSpace.mapMeasurable.map_measurableSpace_eq · cited by 3Measurable.map_measurable…Continuous.map_eq_borelCITED BYCITES

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