`BookProof.NavierStokesFlow.FockContinuum.tendsto_eLpNorm_indicator_compl` (μ : Measure X) {g : X → ℝ} (hg : Measurable g) (f : Lp ℂ 2 μ) : Filter.Tendsto (fun n : ℕ => eLpNorm ({x

Proved

BookProof.NavierStokesFlow.FockContinuum.tendsto_eLpNorm_indicator_compl

by leonardopedro · Oct 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesFockContinuum.

BookProof.NavierStokesFlow.FockContinuum.tendsto_eLpNorm_indicator_compl (μ : Measure X) {g : X → ℝ} (hg : Measurable g) (f : Lp ℂ 2 μ) : Filter.Tendsto (fun n : ℕ => eLpNorm ({x | |g x| ≤ (n : ℝ)}ᶜ.indicator ((f : X → ℂ))) 2 μ) Filter.atTop (nhds 0)

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.FockContinuum.tendsto_eLpNorm_indicator_compl.

Preamble

-- Generated from ChapterNavierStokesFockContinuum.lean — theorem BookProof.NavierStokesFlow.FockContinuum.tendsto_eLpNorm_indicator_compl
import Mathlib
import Definitions.Def_ChapterNavierStokesFockContinuum
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.FockContinuum


open MeasureTheory



open FullEsa

variable {X : Type*} [MeasurableSpace X]

Formal statement

theorem BookProof.NavierStokesFlow.FockContinuum.tendsto_eLpNorm_indicator_compl (μ : Measure X) {g : X → ℝ} (hg : Measurable g)
    (f : Lp ℂ 2 μ) :
    Filter.Tendsto
      (fun n : ℕ => eLpNorm ({x | |g x| ≤ (n : ℝ)}ᶜ.indicator ((f : X → ℂ))) 2 μ)
      Filter.atTop (nhds 0) := by sorry

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