`BookProof.ChapterLpScaleMeasure.memLp_top_smul_measure_iff` (hc0 : c ≠ 0) {f : α → ℂ} : MemLp f ⊤ (c • nu) ↔ MemLp f ⊤ nu

Proved

BookProof.ChapterLpScaleMeasure.memLp_top_smul_measure_iff

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLpScaleMeasure.

BookProof.ChapterLpScaleMeasure.memLp_top_smul_measure_iff (hc0 : c ≠ 0) {f : α → ℂ} : MemLp f ⊤ (c • nu) ↔ MemLp f ⊤ nu

Formalization note: Lean 4 identifier BookProof.ChapterLpScaleMeasure.memLp_top_smul_measure_iff.

Preamble

-- Generated from ChapterLpScaleMeasure.lean — theorem BookProof.ChapterLpScaleMeasure.memLp_top_smul_measure_iff
import Definitions.Def_ChapterLinftyMultiplication
import Mathlib
import Definitions.Def_ChapterLpScaleMeasure
open BookProof.ChapterLpScaleMeasure


noncomputable section

open MeasureTheory ENNReal


open BookProof.ChapterLinftyMultiplication

variable {α : Type*} [MeasurableSpace α] {nu : Measure α} {c : ENNReal}

Formal statement

theorem BookProof.ChapterLpScaleMeasure.memLp_top_smul_measure_iff (hc0 : c ≠ 0) {f : α → ℂ} :
    MemLp f ⊤ (c • nu) ↔ MemLp f ⊤ nu := by sorry

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