`BookProof.NsScalarVectorCurry.enn_tendsto_zero_of_sq` {u : ℕ → ℝ≥0∞} (h : Filter.Tendsto (fun k => u k ^ 2) Filter.atTop (nhds 0)) : Filter.Tendsto u Filter.atTop (nhds 0)

Proved

BookProof.NsScalarVectorCurry.enn_tendsto_zero_of_sq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsScalarVectorCurry.

BookProof.NsScalarVectorCurry.enn_tendsto_zero_of_sq {u : ℕ → ℝ≥0∞} (h : Filter.Tendsto (fun k => u k ^ 2) Filter.atTop (nhds 0)) : Filter.Tendsto u Filter.atTop (nhds 0)

Formalization note: Lean 4 identifier BookProof.NsScalarVectorCurry.enn_tendsto_zero_of_sq.

Preamble

-- Generated from ChapterNsScalarVectorCurry.lean — theorem BookProof.NsScalarVectorCurry.enn_tendsto_zero_of_sq
import Mathlib
import Definitions.Def_ChapterNsScalarVectorCurry
open BookProof.NsScalarVectorCurry


open MeasureTheory Filter Set
open scoped ENNReal ComplexConjugate


noncomputable section

variable {V W : Type*} [MeasurableSpace V] [MeasurableSpace W]
  {μ : Measure V} {ν : Measure W}

variable [SigmaFinite μ] [SigmaFinite ν]

Formal statement

theorem BookProof.NsScalarVectorCurry.enn_tendsto_zero_of_sq {u : ℕ → ℝ≥0∞}
    (h : Filter.Tendsto (fun k => u k ^ 2) Filter.atTop (nhds 0)) :
    Filter.Tendsto u Filter.atTop (nhds 0) := by sorry

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