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Theorems · Theorem · measure theory

Continuous.borel_measurable

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β},
  Continuous f → Measurable f
Defined in
Mathlib.MeasureTheory.Constructions.BorelSpace.Basic
Cited by
3 results in Mathlib
Foundations
Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Continuous.measurable · cited by 181Continuous.measurableprod_le_borel_prod · cited by 1prod_le_borel_prodpi_le_borel_pi · cited by 0pi_le_borel_piSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.ofPred · cited by 6101Set.ofPredSet.preimage · cited by 4946Set.preimageContinuous · cited by 2592ContinuousIsOpen · cited by 2400IsOpenMeasurable · cited by 1499MeasurableIsOpen.preimage · cited by 147IsOpen.preimageborel · cited by 57borelMeasurableSpace.generateFrom_le · cited by 49MeasurableSpace.generateF…Measurable.of_le_map · cited by 6Measurable.of_le_mapContinuous.borel_measurableCITED BYCITES

Cites11

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.