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On the uniqueness of convex-ranged probabilities

Massimiliano Amarante

Title:
On the uniqueness of convex-ranged probabilities
Author(s):
Amarante, Massimiliano
Date:
Type:
Working papers
Department:
Economics
Permanent URL:
Series:
Department of Economics Discussion Papers
Part Number:
0203-24
Publisher:
Department of Economics, Columbia University
Publisher Location:
New York
Abstract:
We provide an alternative proof of a theorem of Marinacci [2] regarding the equality of two convex-ranged measures. Specifically, we show that, if P and Q are two nonatomic, countably additive probabilities on a measurable space (S, Σ), the condition [∃A∗ ∈ Σ with 0 < P(A∗) < 1 such that P(A∗) = P(B)=⇒ Q(A∗) = Q(B) whenever B∈Σ] is equivalent to the condition [∀A,B ∈ Σ P(A) > P(B)=⇒ Q(A) ≥ Q(B)]. Moreover, either one is equivalent to P = Q.
Subject(s):
Economic theory
Item views:
368
Metadata:
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