import Mathlib.MeasureTheory.Order.Lattice
import Mathlib.Probability.Independence.Integration
import Mathlib.Probability.Kernel.Representation
import Mathlib.Probability.Kernel.IonescuTulcea.Traj
import Mathlib.Probability.Process.FiniteDimensionalLaws
import Mathlib.Probability.HasCondDistrib
import Mathlib.MeasureTheory.Measure.ProbabilityMeasure
import Mathlib.Probability.Independence.Basic
import Mathlib.Probability.Independence.Conditional
import Mathlib.MeasureTheory.Measure.SubFinite
import Mathlib.Probability.Kernel.RadonNikodym
import Mathlib.Analysis.Normed.Ring.Basic
import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic
import Mathlib.Probability.Kernel.Composition.MapComap
import Mathlib.Order.CompletePartialOrder
import Mathlib.Probability.Martingale.BorelCantelli
import Mathlib.Probability.IdentDistrib
import Mathlib.Probability.Independence.InfinitePi
import Mathlib.MeasureTheory.Function.FactorsThrough

/-! # Standalone extraction for `Bandits.ArrayModel.probSpace`
Definitions are copied verbatim; theorem proofs are replaced by `sorry`.
Auto-generated by Referee. -/

set_option quotPrecheck false

-- Namespace stubs (so later `open`s resolve).
namespace Finset
end Finset
namespace MeasureTheory
end MeasureTheory
namespace ProbabilityTheory
end ProbabilityTheory
namespace Learning
end Learning
namespace ENNReal
end ENNReal
namespace Bandits
end Bandits
namespace Bandits.ArrayModel
end Bandits.ArrayModel

-- ═══ ForMathlib.MeasureTheory.Order.Lattice ═══
section
open Finset
variable {α δ : Type*} [MeasurableSpace δ] [SemilatticeInf α] {m : MeasurableSpace α} [MeasurableInf₂ α]
attribute [to_dual existing] MeasurableInf₂
end

-- ═══ Online.Bandit.ArrayProbSpace ═══
section
open MeasureTheory ProbabilityTheory Filter Real Finset Learning
open scoped ENNReal NNReal
namespace Bandits
variable {𝓐 R : Type*} {m𝓐 : MeasurableSpace 𝓐} {mR : MeasurableSpace R}
section MeasureSpace
namespace ArrayModel
open unitInterval
section ProbabilitySpace

variable (𝓐 R) in
/-- Probability space for the array model of stochastic bandits. -/
def probSpace : Type _ := (ℕ → I) × (ℕ → 𝓐 → R)

variable [Nonempty 𝓐] [StandardBorelSpace 𝓐]
end ProbabilitySpace
variable [Nonempty 𝓐] [StandardBorelSpace 𝓐]
variable [DecidableEq 𝓐]
end ArrayModel
end MeasureSpace
end Bandits
end