`BookProof.WeylCauchyRiemann.integral_complex_eq_prod` (G : ℂ → ℂ) : ∫ z : ℂ, G z = ∫ p : ℝ × ℝ, G (p.1 + p.2 * Complex.I)

Proved

BookProof.WeylCauchyRiemann.integral_complex_eq_prod

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWeylCauchyRiemann.

BookProof.WeylCauchyRiemann.integral_complex_eq_prod (G : ℂ → ℂ) : ∫ z : ℂ, G z = ∫ p : ℝ × ℝ, G (p.1 + p.2 * Complex.I)

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

Preamble

-- Generated from ChapterWeylCauchyRiemann.lean — theorem BookProof.WeylCauchyRiemann.integral_complex_eq_prod
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.integral_complex_eq_prod (G : ℂ → ℂ) :
    ∫ z : ℂ, G z = ∫ p : ℝ × ℝ, G (p.1 + p.2 * Complex.I) := by sorry

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