`BookProof.ChapterGaugeCasimirAverage.gaugeAverage_const` (μ : Measure G) [IsProbabilityMeasure μ] (c : ℝ) : gaugeAverage (X := X) μ (fun _ => c) = fun _ => c

Proved

BookProof.ChapterGaugeCasimirAverage.gaugeAverage_const

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaugeCasimirAverage.

BookProof.ChapterGaugeCasimirAverage.gaugeAverage_const (μ : Measure G) [IsProbabilityMeasure μ] (c : ℝ) : gaugeAverage (X := X) μ (fun _ => c) = fun _ => c

Formalization note: Lean 4 identifier BookProof.ChapterGaugeCasimirAverage.gaugeAverage_const.

Preamble

-- Generated from ChapterGaugeCasimirAverage.lean — theorem BookProof.ChapterGaugeCasimirAverage.gaugeAverage_const
import Definitions.Def_ChapterGaugeIncompleteFixing
import Mathlib
import Definitions.Def_ChapterGaugeCasimirAverage
open BookProof.ChapterGaugeCasimirAverage



open BookProof.ChapterGaugeIncompleteFixing
open MeasureTheory
open scoped InnerProductSpace

variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℂ V]
variable {ι : Type*} [Fintype ι]
variable {X : Type*}
variable {G : Type*} [Group G] [MeasurableSpace G] [MeasurableMul G] [MulAction G X]

Formal statement

theorem BookProof.ChapterGaugeCasimirAverage.gaugeAverage_const (μ : Measure G) [IsProbabilityMeasure μ] (c : ℝ) :
    gaugeAverage (X := X) μ (fun _ => c) = fun _ => c := by sorry

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