`BookProof.NsFieldMomentumInverse.mem_momDomain_iff` {m : W} (f : Lp ℂ 2 (volume : Measure W)) : f ∈ momDomain m ↔ ∃ g, IsMomInverse m f g

Proved

BookProof.NsFieldMomentumInverse.mem_momDomain_iff

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsFieldMomentumInverse.

BookProof.NsFieldMomentumInverse.mem_momDomain_iff {m : W} (f : Lp ℂ 2 (volume : Measure W)) : f ∈ momDomain m ↔ ∃ g, IsMomInverse m f g

Formalization note: Lean 4 identifier BookProof.NsFieldMomentumInverse.mem_momDomain_iff.

Preamble

-- Generated from ChapterNsFieldMomentumInverse.lean — theorem BookProof.NsFieldMomentumInverse.mem_momDomain_iff
import Definitions.Def_ChapterNsSpatialMomentumMultiplier
import Definitions.Def_ChapterFourierMultiplierEsa
import Definitions.Def_ChapterStrichartzWave
import Mathlib
import Definitions.Def_ChapterNsFieldMomentumInverse
open BookProof.NsFieldMomentumInverse



open MeasureTheory SchwartzMap FourierTransform
open BookProof.NsSpatialMultiplier BookProof.FourierMultiplierEsa BookProof.StrichartzWave

noncomputable section

variable {W : Type*} [NormedAddCommGroup W] [InnerProductSpace ℝ W] [FiniteDimensional ℝ W]
  [MeasurableSpace W] [BorelSpace W]

Formal statement

theorem BookProof.NsFieldMomentumInverse.mem_momDomain_iff {m : W} (f : Lp ℂ 2 (volume : Measure W)) :
    f ∈ momDomain m ↔ ∃ g, IsMomInverse m f g := by sorry

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