Theorems · Theorem · measure theory
measurableSet_preimage
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {m : MeasurableSpace α} {mβ : MeasurableSpace β} {t : Set β},
Measurable f → MeasurableSet t → MeasurableSet (f ⁻¹' t)- Cited by
- 7 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- Set.preimagestatement · cited by 4,946
- MeasurableSetstatement and proof · cited by 3,075
- Measurablestatement and proof · cited by 1,499
Cited by7
Results whose statement or proof uses this declaration.
- ProbabilityTheory.Kernel.singularPart_compl_mutuallySingularSetSliceproof · cited by 4
- ZSpan.fundamentalDomain_measurableSetproof · cited by 3
- PMF.toMeasure_map_applyproof · cited by 1
- MeasureTheory.measurableSet_prodMk_add_one_of_predictableproof · cited by 1
- ProbabilityTheory.HasCondDistrib.comp_rightproof · cited by 1