Theorems · Theorem · measure theory
MeasureTheory.AEStronglyMeasurable.isSeparable_ae_range
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace β] {m₀ : MeasurableSpace α} {μ : MeasureTheory.Measure α}
{f : α → β}, MeasureTheory.AEStronglyMeasurable f μ → ∃ t, TopologicalSpace.IsSeparable t ∧ ∀ᵐ (x : α) ∂μ, f x ∈ t- Cited by
- 4 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Set.rangeproof · cited by 4,705
- Filter.Eventuallystatement · cited by 3,134
- MeasureTheory.aestatement · cited by 2,352
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- MeasureTheory.AEStronglyMeasurablestatement and proof · cited by 755
- MeasureTheory.AEStronglyMeasurable.mkproof · cited by 82
- MeasureTheory.AEStronglyMeasurable.ae_eq_mkproof · cited by 77
Cited by4
Results whose statement or proof uses this declaration.
- aestronglyMeasurable_iff_aemeasurable_separableproof · cited by 10
- MeasureTheory.AEStronglyMeasurable.aestronglyMeasurable_id_mapproof · cited by 2
- MeasureTheory.ae_eq_zero_restrict_of_forall_setIntegral_eq_zeroproof · cited by 2
- QuasiErgodic.ae_eq_const_of_ae_eq_comp_aeproof · cited by 2