`BookProof.ChapterLinftyMaximalAbelian.multOp_indicator_oneLp` {s : Set α} (hs : MeasurableSet s) (c : ℂ) : multOp (s.indicator fun _ => c) ((memLp_top_const c).indicator hs) (oneL

Proved

BookProof.ChapterLinftyMaximalAbelian.multOp_indicator_oneLp

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLinftyMaximalAbelian.

BookProof.ChapterLinftyMaximalAbelian.multOp_indicator_oneLp {s : Set α} (hs : MeasurableSet s) (c : ℂ) : multOp (s.indicator fun _ => c) ((memLp_top_const c).indicator hs) (oneLp μ) = indicatorConstLp 2 hs (measure_ne_top μ s) c

Formalization note: Lean 4 identifier BookProof.ChapterLinftyMaximalAbelian.multOp_indicator_oneLp.

Preamble

-- Generated from ChapterLinftyMaximalAbelian.lean — theorem BookProof.ChapterLinftyMaximalAbelian.multOp_indicator_oneLp
import Mathlib
import Definitions.Def_ChapterLinftyMaximalAbelian
import Definitions.Def_ChapterLinftyMultiplication
open BookProof.ChapterLinftyMultiplication
open BookProof.ChapterLinftyMaximalAbelian


noncomputable section

open MeasureTheory ENNReal Complex


open BookProof.ChapterLinftyMultiplication

variable {α : Type*} [MeasurableSpace α] {μ : Measure α} [IsFiniteMeasure μ]

Formal statement

theorem BookProof.ChapterLinftyMaximalAbelian.multOp_indicator_oneLp {s : Set α} (hs : MeasurableSet s) (c : ℂ) :
    multOp (s.indicator fun _ => c) ((memLp_top_const c).indicator hs) (oneLp μ)
      = indicatorConstLp 2 hs (measure_ne_top μ s) c := by sorry

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