Indicator integrand for a time interval

Definition

KLSModular_LevyStochCalc_Brownian_ItoIncrement

by Lazyfill · Oct 25, 2026 · Mathlib 0df444a (Lean v4.33.1)

functional-inequalitiesklskls-conjecturekls-modularlog-concavemodule-contextvendored-levystochcalc

Vendored from the LevyStochCalc library at https://github.com/cgarryZA/LevyStochCalc, commit 984dbf0b790031eac05d56fe5a84b65e15e1e932. indIoc Ω a b is the process independent of $\omega$ whose time profile is the indicator $1_{(a,b]}$ with values in $\mathbb R$ .

Original module imports

import LevyStochCalc.Brownian.ItoAlgebra

Original declaration excerpt

Shown in the original module context.

noncomputable def indIoc (Ω) [MeasurableSpace Ω] (a b : ℝ) : Ω → ℝ → ℝ :=
  fun _ s => (Set.Ioc a b).indicator (fun _ => (1 : ℝ)) s

Module navigation

Direct project imports: LevyStochCalc/Brownian/ItoAlgebra.

Project result: The KLS conjecture.

Original module · LevyStochCalc.Brownian.ItoIncrement · Frozen source 408915f.

Definition code

import Definitions.Def_KLSModular_LevyStochCalc_Brownian_ItoAlgebra

/-
Copyright (c) 2026 Christian Garry. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Garry
-/
-- Vendored from https://github.com/cgarryZA/LevyStochCalc at commit 984dbf0b790031eac05d56fe5a84b65e15e1e932 (upstream path LevyStochCalc/Brownian/ItoIncrement.lean; Apache-2.0; provenance in formalization/vendor/vendor-lock.json of the KLS repository)
namespace LevyStochCalc
namespace Brownian
namespace Ito
open MeasureTheory ProbabilityTheory
open scoped NNReal ENNReal
universe u
variable {Ω : Type u} [MeasurableSpace Ω]
section Indicator
/-- The indicator integrand of a time window, as a process constant in the sample point. -/
noncomputable def indIoc (Ω) [MeasurableSpace Ω] (a b : ℝ) : Ω → ℝ → ℝ :=
  fun _ s => (Set.Ioc a b).indicator (fun _ => (1 : ℝ)) s
variable {P : Measure Ω} [IsProbabilityMeasure P] (W : LevyStochCalc.Brownian.BrownianMotion P)
  (ℱ : Filtration ℝ ‹MeasurableSpace Ω›) (hℱ : IsBrownianFiltration W ℱ)
end Indicator
end Ito
end Brownian
end LevyStochCalc

Source

Lean source: https://github.com/cgarryZA/LevyStochCalc/blob/984dbf0b790031eac05d56fe5a84b65e15e1e932/LevyStochCalc/Brownian/ItoIncrement.lean#L26-L28 (repository human-ai-mathematics/kls-lean, commit 408915f, module `LevyStochCalc.Brownian.ItoIncrement`, definition bundle `KLSModular_LevyStochCalc_Brownian_ItoIncrement`; the repository is private at upload time). Vendored from https://github.com/cgarryZA/LevyStochCalc at commit 984dbf0b790031eac05d56fe5a84b65e15e1e932 (Apache-2.0; upstream copyright notice retained in the Lean text).

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