translation invariance and finite additivity in a probability measure on the natural numbers
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ID: 153936
2002
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Abstract
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.
| Reference Key |
gardner2002internationaltranslation
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|---|---|
| Authors | ;Robert Gardner;Robert Price |
| Journal | structural engineering and mechanics |
| Year | 2002 |
| DOI |
10.1155/S0161171202007494
|
| URL | |
| Keywords |
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