Prove2Me

`BookProof.ChapterDiffuseCdfModel.continuous_cdf_of_noAtoms` [IsProbabilityMeasure mu] [NullSingletonClass mu] : Continuous (cdf mu)

Proved
BookProof.ChapterDiffuseCdfModel.continuous_cdf_of_noAtoms

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterDiffuseCdfModel.

BookProof.ChapterDiffuseCdfModel.continuous_cdf_of_noAtoms [IsProbabilityMeasure mu] [NullSingletonClass mu] : Continuous (cdf mu)

Formalization note: Lean 4 identifier BookProof.ChapterDiffuseCdfModel.continuous_cdf_of_noAtoms.

Preamble
-- Generated from ChapterDiffuseCdfModel.lean — theorem BookProof.ChapterDiffuseCdfModel.continuous_cdf_of_noAtoms
import Mathlib
import Definitions.Def_ChapterDiffuseCdfModel
open BookProof.ChapterDiffuseCdfModel


noncomputable section

open MeasureTheory ProbabilityTheory Filter


variable (mu : Measure ℝ)
Formal statement
theorem BookProof.ChapterDiffuseCdfModel.continuous_cdf_of_noAtoms [IsProbabilityMeasure mu] [NullSingletonClass mu] :
    Continuous (cdf mu) := by sorry

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