In the ‘Generalizing ≤_st: The ≼-Ordering’ subsection of ‘The Decision Framework’, there is an error in Lemma 2, Theorem 1 and Theorem 2, and additional hypotheses are included.

For Lemma 2, the correct hypothesis is: For any two probability distributions F₁, F₂ and associated random variables R₁ ∼ F₁, R₂ ∼ F₂, according to Definition 1. Let F₁, F₂ be jointly supported on a compact set Ω=[0,a] and let the respective density functions f₁, f₂ satisfy f₁(a)≠f₂(a). Then, there exists a number so that either [∀k ≥ K: m_R1(k) ≤ m_R2(k)] or [∀k ≥ K: m_R1(k) ≥ m_R2(k)].

For Theorem 1, the correct hypothesis is: Let be according to definition 1. Assume every element X ∈ to be represented by hyperreal number , where is any free ultrafilter. Let X, Y ∈ be arbitrary, and satisfying the hypothesis of Lemma 2 with . Then, X ≼ Y if x ≤ y in , irrespectively of .

For Theorem 2, the correct hypothesis is: Let X, Y ∈ have the distributions F₁, F₂ satisfying the hypothesis of Lemma 2. If X ≼ Y, then there exists a threshold so that for every , we have .

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