`BookProof.ChapterIrreversible.entropy_eq_zero_iff_pointMass` (p : Fin n → ℝ) (hnn : ∀ a, 0 ≤ p a) (hsum : ∑ a, p a = 1) : entropy p = 0 ↔ IsPointMass p

Proved

BookProof.ChapterIrreversible.entropy_eq_zero_iff_pointMass

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterIrreversible.

BookProof.ChapterIrreversible.entropy_eq_zero_iff_pointMass (p : Fin n → ℝ) (hnn : ∀ a, 0 ≤ p a) (hsum : ∑ a, p a = 1) : entropy p = 0 ↔ IsPointMass p

Formalization note: Lean 4 identifier BookProof.ChapterIrreversible.entropy_eq_zero_iff_pointMass.

Preamble

-- Generated from ChapterIrreversible.lean — theorem BookProof.ChapterIrreversible.entropy_eq_zero_iff_pointMass
import Mathlib
import Definitions.Def_ChapterIrreversible
open BookProof.ChapterIrreversible


open scoped BigOperators
open Finset


variable {n : ℕ}

Formal statement

theorem BookProof.ChapterIrreversible.entropy_eq_zero_iff_pointMass (p : Fin n → ℝ) (hnn : ∀ a, 0 ≤ p a)
    (hsum : ∑ a, p a = 1) : entropy p = 0 ↔ IsPointMass p := by sorry

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