`BookProof.WeylCauchyRiemann.ae_tendsto_mollify_bump` {F : ℂ → ℂ} (hF : LocallyIntegrable F) : ∀ᵐ z : ℂ, Tendsto (fun n => mollify F ((bumpSeq n).normed volume) z) atTop (nhds (F z

Proved

BookProof.WeylCauchyRiemann.ae_tendsto_mollify_bump

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeylCauchyRiemann.

BookProof.WeylCauchyRiemann.ae_tendsto_mollify_bump {F : ℂ → ℂ} (hF : LocallyIntegrable F) : ∀ᵐ z : ℂ, Tendsto (fun n => mollify F ((bumpSeq n).normed volume) z) atTop (nhds (F z))

Formalization note: Lean 4 identifier BookProof.WeylCauchyRiemann.ae_tendsto_mollify_bump.

Preamble

-- Generated from ChapterWeylCauchyRiemann.lean — theorem BookProof.WeylCauchyRiemann.ae_tendsto_mollify_bump
import Definitions.Def_ChapterRadialMollifier
import Mathlib
import Definitions.Def_ChapterWeylCauchyRiemann
open BookProof.WeylCauchyRiemann



open MeasureTheory Metric Set Filter Complex BookProof.RadialMollifier
open scoped Convolution Topology ContDiff

noncomputable section

Formal statement

theorem BookProof.WeylCauchyRiemann.ae_tendsto_mollify_bump {F : ℂ → ℂ} (hF : LocallyIntegrable F) :
    ∀ᵐ z : ℂ, Tendsto (fun n => mollify F ((bumpSeq n).normed volume) z) atTop (nhds (F z)) := by sorry

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