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Inspired by the "two envelopes exchange paradox," a finitely additive probability measure m on the natural numbers is introduced. The measure is uniform in the sense that m ((i))=m ((j)) for all i, j∈□. The measure is shown to be translation invariant and has such desirable properties as m ((i∈□| i=0 (mod2)))=1/2. For any r∈ [0, 1], a set A is constructed such that m (A)=r; however, m is not defined on the power set of □. Finally, a resolution to the two envelopes exchange paradox is presented in terms of m.

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Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Creative Commons License

Creative Commons Attribution 3.0 License
This work is licensed under a Creative Commons Attribution 3.0 License.