`BookProof.NsScalarVectorCurry.ae_tendsto_zero_of_tsum_lintegral_ne_top` {X : Type*} [MeasurableSpace X] {ρ : Measure X} (ψ : ℕ → X → ℝ≥0∞) (hmeas : ∀ k, AEMeasurable (ψ k) ρ) (h :

Proved

BookProof.NsScalarVectorCurry.ae_tendsto_zero_of_tsum_lintegral_ne_top

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsScalarVectorCurry.

BookProof.NsScalarVectorCurry.ae_tendsto_zero_of_tsum_lintegral_ne_top {X : Type*} [MeasurableSpace X] {ρ : Measure X} (ψ : ℕ → X → ℝ≥0∞) (hmeas : ∀ k, AEMeasurable (ψ k) ρ) (h : ∑' k, ∫⁻ x, ψ k x ∂ρ ≠ ∞) : ∀ᵐ x ∂ρ, Filter.Tendsto (fun k => ψ k x) Filter.atTop (nhds 0)

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

Preamble

-- Generated from ChapterNsScalarVectorCurry.lean — theorem BookProof.NsScalarVectorCurry.ae_tendsto_zero_of_tsum_lintegral_ne_top
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.ae_tendsto_zero_of_tsum_lintegral_ne_top {X : Type*} [MeasurableSpace X] {ρ : Measure X}
    (ψ : ℕ → X → ℝ≥0∞) (hmeas : ∀ k, AEMeasurable (ψ k) ρ)
    (h : ∑' k, ∫⁻ x, ψ k x ∂ρ ≠ ∞) :
    ∀ᵐ x ∂ρ, Filter.Tendsto (fun k => ψ k x) Filter.atTop (nhds 0) := by sorry

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