Dyadic approximation from below

Definition

KLSModular_LevyStochCalc_Brownian_ItoVersionExists

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. dyadicApprox n u is $\lfloor u2^n\rfloor_+/2^n$ , the nonnegative-floor dyadic approximation from below to the real number $u$ at level $n$ .

Original module imports

import LevyStochCalc.Brownian.ItoProcessVersion
import LevyStochCalc.Brownian.ItoQuadVarSum
import LevyStochCalc.Brownian.AugmentedFiltration

Original declaration excerpt

Shown in the original module context.

noncomputable def dyadicApprox (n : ℕ) (u : ℝ) : ℝ := (⌊u * 2 ^ n⌋₊ : ℝ) / 2 ^ n

Module navigation

Direct project imports: LevyStochCalc/Brownian/ItoProcessVersion, LevyStochCalc/Brownian/ItoQuadVarSum, LevyStochCalc/Brownian/AugmentedFiltration.

Theorems in source order:

exists_continuousAdapted_modification

Project result: The KLS conjecture.

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

Definition code

import Definitions.Def_KLSModular_LevyStochCalc_Brownian_ItoProcessVersion
import Definitions.Def_KLSModular_LevyStochCalc_Brownian_ItoQuadVarSum
import Definitions.Def_KLSModular_LevyStochCalc_Brownian_AugmentedFiltration

/-
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/ItoVersionExists.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]
/-- The `n`-th dyadic approximation from below of a nonnegative real. -/
noncomputable def dyadicApprox (n : ℕ) (u : ℝ) : ℝ := (⌊u * 2 ^ n⌋₊ : ℝ) / 2 ^ n
end Ito
end Brownian
end LevyStochCalc

Source

Lean source: https://github.com/cgarryZA/LevyStochCalc/blob/984dbf0b790031eac05d56fe5a84b65e15e1e932/LevyStochCalc/Brownian/ItoVersionExists.lean#L69-L70 (repository human-ai-mathematics/kls-lean, commit 408915f, module `LevyStochCalc.Brownian.ItoVersionExists`, definition bundle `KLSModular_LevyStochCalc_Brownian_ItoVersionExists`; 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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