Correction to: Level-2 Large Deviation Principle for Countable Markov Shifts Without Gibbs States (Journal of Statistical Physics, (2023), 190, 7, (120), 10.1007/s10955-023-03126-2)

Since the measure μ₀ constructed in the proof of [1, Lemma 3.2] depends on n, the statement of [1, Proposition J] is incorrect. The correct statement is as follows. Let ϕ:X→R be acceptable and satisfy P(ϕ)<∞. Let ℓ≥1, φ→∈C_u(X)^ℓ, α→∈R^ℓ and let C⊂M(X) be a non-empty closed set of the form (Formula presented.) For any ε>0 there exists n₀≥1 such that for every n≥n₀, there exists μ∈M_ϕ(X,σ) such that ∫φ→dμ>α→-ε→ and (Formula presented.) The proof of Proposition J remains intact. At the end of the proof we consider sufficiently large n, without letting n→∞. The phrase ‘By Lemma 3.2’ in the third paragraph of Sect. 3.3 should be replaced by ‘By Proposition J’.