On the uniqueness of convexranged probabilities
 Title:
 On the uniqueness of convexranged probabilities
 Author(s):
 Amarante, Massimiliano
 Date:
 2003
 Type:
 Working papers
 Department(s):
 Economics
 Persistent URL:
 http://hdl.handle.net/10022/AC:P:504
 Series:
 Department of Economics Discussion Papers
 Part Number:
 020324
 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 convexranged 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
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 Suggested Citation:
 Massimiliano Amarante, 2003, On the uniqueness of convexranged probabilities, Columbia University Academic Commons, http://hdl.handle.net/10022/AC:P:504.