Theorems · Theorem · measure theory
Continuous.aemeasurable
∀ {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 → ∀ {μ : MeasureTheory.Measure α}, AEMeasurable f μA continuous function from an OpensMeasurableSpace to a BorelSpace
is ae-measurable.
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Continuousstatement and proof · cited by 2,592
- BorelSpacestatement and proof · cited by 1,602
- AEMeasurablestatement · cited by 840
- OpensMeasurableSpacestatement and proof · cited by 636
- Measurable.aemeasurableproof · cited by 304
- Continuous.measurableproof · cited by 181
Cited by21
Results whose statement or proof uses this declaration.
- ProbabilityTheory.IsGaussianProcess.isPreBrownianReal_of_covarianceproof · cited by 4
- MeasureTheory.TendstoInDistribution.continuous_compproof · cited by 3
- MeasureTheory.Measure.InnerRegular.map_of_continuousproof · cited by 2
- ContinuousLinearMap.integral_id_mapproof · cited by 2
- QuotientGroup.integral_eq_integral_automorphizeproof · cited by 1
- MeasureTheory.ae_comp_linearMap_mem_iffproof · cited by 1
- ProbabilityTheory.integral_linearMap_gaussianRealproof · cited by 1
- MeasureTheory.measureReal_abs_inner_gt_le_integral_charFunproof · cited by 1
- ProbabilityTheory.HasGaussianLaw.charFun_map_eqproof · cited by 1
- ProbabilityTheory.variance_dual_stdGaussianproof · cited by 1
- MeasureTheory.tendstoInDistribution_of_ae_tendstoproof · cited by 1