Mathlib Map

Theorems · Theorem · measure theory

BorelSpace.measurable_eq

∀ {α : Type u_6} {inst : TopologicalSpace α} {inst_1 : MeasurableSpace α} [self : BorelSpace α], inst_1 = borel α

The measurable sets are exactly the Borel-measurable sets.

Defined in
Mathlib.MeasureTheory.Constructions.BorelSpace.Basic
Cited by
26 results in Mathlib
Foundations
Depth 9 from the axioms · uses no axioms
Assumes
BorelSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Continuous.measurable · cited by 181Continuous.measurableMeasurableSet.induction_on_open · cited by 7MeasurableSet.induction_o…dimH_def · cited by 5dimH_defmeasurable_of_Ioi · cited by 4measurable_of_Ioimeasurable_of_isOpen · cited by 3measurable_of_isOpenMeasureTheory.Measure.addModularCharacterFun_eq_addHaarScalarFactor · cited by 3Measure.addModularCharact…eq_borel_upgradeStandardBorel · cited by 3eq_borel_upgradeStandardB…MeasureTheory.Measure.modularCharacterFun_eq_haarScalarFactor · cited by 3Measure.modularCharacterF…Measurable.isLUB · cited by 3Measurable.isLUBexists_opensMeasurableSpace_of_countablySeparated · cited by 2exists_opensMeasurableSpa…measurable_of_Iio · cited by 2measurable_of_IioMeasureTheory.Measure.measurePreserving_homeomorphUnitSphereProd · cited by 2Measure.measurePreserving…MeasureTheory.addHaarScalarFactor_smul_eq_distribHaarChar · cited by 2MeasureTheory.addHaarScal…MeasureTheory.ext_of_forall_lintegral_eq_of_IsFiniteMeasure · cited by 2MeasureTheory.ext_of_fora…MeasureTheory.Measure.ext_of_Ico' · cited by 2Measure.ext_of_Ico'TopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceBorelSpace · cited by 1602BorelSpaceborel · cited by 57borelBorelSpace.measurable_eqCITED BYCITES

Cites4

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

Cited by26

Results whose statement or proof uses this declaration.