Theorems · Theorem · measure theory

measurable_of_Iio

∀ {α : Type u_1} {δ : Type u_4} [inst : TopologicalSpace α] {mα : MeasurableSpace α} [BorelSpace α]
  {mδ : MeasurableSpace δ} [inst_2 : LinearOrder α] [OrderTopology α] [SecondCountableTopology α] {f : δ → α},
  (∀ (x : α), MeasurableSet (f ⁻¹' Set.Iio x)) → Measurable f

Defined in: Mathlib.MeasureTheory.Constructions.BorelSpace.Order
Cited by: 2 results in Mathlib
Foundations: Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace BorelSpace LinearOrder OrderTopology SecondCountableTopology

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Cites16

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

Setproof · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
MeasurableSpacestatement and proof · cited by 13,106
LinearOrderstatement and proof · cited by 8,572
Set.preimagestatement and proof · cited by 4,946
Set.rangeproof · cited by 4,705
MeasurableSetstatement and proof · cited by 3,075
BorelSpacestatement and proof · cited by 1,602
Measurablestatement and proof · cited by 1,499
OrderTopologystatement and proof · cited by 1,355
Set.Iiostatement and proof · cited by 1,166
SecondCountableTopologystatement and proof · cited by 750

Cited by2

Results whose statement or proof uses this declaration.

UpperSemicontinuous.measurableproof · cited by 2
measurable_of_Iciproof · cited by 0