`BookProof.NavierStokesFlow.FockContinuum.mem_boundedEnergyCore` {μ : Measure X} {g : X → ℝ} {f : Lp ℂ 2 μ} : f ∈ boundedEnergyCore μ g ↔ ∃ n : ℕ, ∀ᵐ x ∂μ, ¬ (|g x| ≤...

Proved

BookProof.NavierStokesFlow.FockContinuum.mem_boundedEnergyCore

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesFockContinuum.

BookProof.NavierStokesFlow.FockContinuum.mem_boundedEnergyCore {μ : Measure X} {g : X → ℝ} {f : Lp ℂ 2 μ} : f ∈ boundedEnergyCore μ g ↔ ∃ n : ℕ, ∀ᵐ x ∂μ, ¬ (|g x| ≤ (n : ℝ)) → (f : X → ℂ) x = 0

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

Preamble

-- Generated from ChapterNavierStokesFockContinuum.lean — theorem BookProof.NavierStokesFlow.FockContinuum.mem_boundedEnergyCore
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.mem_boundedEnergyCore {μ : Measure X} {g : X → ℝ} {f : Lp ℂ 2 μ} :
    f ∈ boundedEnergyCore μ g ↔ ∃ n : ℕ, ∀ᵐ x ∂μ, ¬ (|g x| ≤ (n : ℝ)) → (f : X → ℂ) x = 0 := by sorry

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