Translation invariance and finite additivity in a probability measure on the natural numbers
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∈ℕ. The measure is shown to be translation invariant and has such desirable properties as m({i∈ℕ|i≡0(mod2...
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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202007494 |
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| _version_ | 1832552293244862464 |
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| author | Robert Gardner Robert Price |
| author_facet | Robert Gardner Robert Price |
| author_sort | Robert Gardner |
| collection | DOAJ |
| 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∈ℕ. The measure is
shown to be translation invariant and has such desirable
properties as m({i∈ℕ|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 ℕ. Finally, a resolution to the two envelopes exchange paradox is presented in terms of m. |
| format | Article |
| id | doaj-art-58590c4387194ec184418c99c9d76dc0 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-58590c4387194ec184418c99c9d76dc02025-02-03T05:59:06ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-01291058558910.1155/S0161171202007494Translation invariance and finite additivity in a probability measure on the natural numbersRobert Gardner0Robert Price1Department of Mathematics, Box 70663, East Tennessee State University, Johnson City 37614, TN, USADepartment of Mathematics, Box 70663, East Tennessee State University, Johnson City 37614, TN, USAInspired 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∈ℕ. The measure is shown to be translation invariant and has such desirable properties as m({i∈ℕ|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 ℕ. Finally, a resolution to the two envelopes exchange paradox is presented in terms of m.http://dx.doi.org/10.1155/S0161171202007494 |
| spellingShingle | Robert Gardner Robert Price Translation invariance and finite additivity in a probability measure on the natural numbers International Journal of Mathematics and Mathematical Sciences |
| title | Translation invariance and finite additivity in a probability
measure on the natural numbers |
| title_full | Translation invariance and finite additivity in a probability
measure on the natural numbers |
| title_fullStr | Translation invariance and finite additivity in a probability
measure on the natural numbers |
| title_full_unstemmed | Translation invariance and finite additivity in a probability
measure on the natural numbers |
| title_short | Translation invariance and finite additivity in a probability
measure on the natural numbers |
| title_sort | translation invariance and finite additivity in a probability measure on the natural numbers |
| url | http://dx.doi.org/10.1155/S0161171202007494 |
| work_keys_str_mv | AT robertgardner translationinvarianceandfiniteadditivityinaprobabilitymeasureonthenaturalnumbers AT robertprice translationinvarianceandfiniteadditivityinaprobabilitymeasureonthenaturalnumbers |