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},
MeasurableSet t → Measurable f → MeasurableSet (f ⁻¹' t)- Cited by
- 37 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 by37
Results whose statement or proof uses this declaration.
- measurableSet_eq_funproof · cited by 5
- ProbabilityTheory.Kernel.measure_mutuallySingularSetSliceproof · cited by 4
- MeasureTheory.Measure.mconv_absolutelyContinuousproof · cited by 3
- Measurable.eq_constproof · cited by 3
- MeasureTheory.Measure.conv_absolutelyContinuousproof · cited by 3
- MeasureTheory.isTightMeasureSet_range_of_tendsto_limsup_innerproof · cited by 2
- ProbabilityTheory.Kernel.partialTraj_compProd_trajproof · cited by 2
- MeasureTheory.StronglyMeasurable.inv₀proof · cited by 2
- MeasureTheory.measurable_stoppedValueproof · cited by 2
- measurableSet_tendstoproof · cited by 2
- MeasureTheory.measureReal_abs_gt_le_integral_charFunproof · cited by 2
- MeasureTheory.piContent_eq_measure_piproof · cited by 1