`BookProof.CarlemanUnboundedHop.summable_cutMass` (hu : Summable fun n => ‖u n‖ ^ 2) (hΘ0 : ∀ j, 0 ≤ Θ j) (hΘsum : Summable Θ) : Summable (fun N => cutMass u Θ N)

Proved

BookProof.CarlemanUnboundedHop.summable_cutMass

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCarlemanUnboundedHop.

BookProof.CarlemanUnboundedHop.summable_cutMass (hu : Summable fun n => ‖u n‖ ^ 2) (hΘ0 : ∀ j, 0 ≤ Θ j) (hΘsum : Summable Θ) : Summable (fun N => cutMass u Θ N)

Formalization note: Lean 4 identifier BookProof.CarlemanUnboundedHop.summable_cutMass.

Preamble

-- Generated from ChapterCarlemanUnboundedHop.lean — theorem BookProof.CarlemanUnboundedHop.summable_cutMass
import Mathlib
import Definitions.Def_ChapterCarlemanUnboundedHop
open BookProof.CarlemanUnboundedHop



open Finset

noncomputable section

variable {a : ℕ → ℕ → ℂ} {u : ℕ → ℂ} {A θ Θ : ℕ → ℝ}

Formal statement

theorem BookProof.CarlemanUnboundedHop.summable_cutMass (hu : Summable fun n => ‖u n‖ ^ 2) (hΘ0 : ∀ j, 0 ≤ Θ j)
    (hΘsum : Summable Θ) : Summable (fun N => cutMass u Θ N) := by sorry

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