Document Type
Article
Publication Date
1-1-2002
Description
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.
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.
Citation Information
Gardner, Robert; and Price, Robert. 2002. Translation Invariance and Finite Additivity in a Probability Measure on the Natural Numbers. International Journal of Mathematics and Mathematical Sciences. Vol.29(10). 585-589. https://doi.org/10.1155/S0161171202007494 ISSN: 0161-1712
Copyright Statement
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.