Theorems · Theorem · measure theory

Antitone.measurable

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] {mα : MeasurableSpace α} [BorelSpace α]
  [inst_2 : TopologicalSpace β] {mβ : MeasurableSpace β} [BorelSpace β] [inst_4 : LinearOrder α] [OrderTopology α]
  [SecondCountableTopology α] [inst : LinearOrder β] [OrderClosedTopology β] {f : β → α}, Antitone f → Measurable f

Defined in: Mathlib.MeasureTheory.Constructions.BorelSpace.Order
Cited by: 4 results in Mathlib
Foundations: Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace BorelSpace TopologicalSpace BorelSpace LinearOrder OrderTopology SecondCountableTopology LinearOrder OrderClosedTopology

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Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites10

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
LinearOrderstatement and proof · cited by 8,572
BorelSpacestatement and proof · cited by 1,602
Measurablestatement · cited by 1,499
OrderTopologystatement and proof · cited by 1,355
SecondCountableTopologystatement and proof · cited by 750
Antitonestatement and proof · cited by 563
OrderClosedTopologystatement and proof · cited by 445
Monotone.measurableproof · cited by 2

Cited by4

Results whose statement or proof uses this declaration.

MeasureTheory.lintegral_le_liminf_lintegral_of_forall_isOpen_measure_le_liminf_measureproof · cited by 1
MeasureTheory.tendsto_integral_meas_thickening_leproof · cited by 1
MeasureTheory.Integrable.integral_eq_integral_meas_ltproof · cited by 1
MeasureTheory.BoundedContinuousFunction.integral_le_of_levyProkhorovEDist_ltproof · cited by 1