Kelley's theorem from the duality of LP and Tychonoff's theorem

Year, pages: 2002, 309 - 314

Many mathematical problems can be reformulated as optimization problems. In the present paper we shall see how a problem on the existence of strictly positive finitely additive probabilities can be considered as an optimization problem. We use the duality of Linear Programming and Tychonoff's theorem in general topology and derive a 1959 result of J. L. Kelley on the existence of strictly positive probability charges on Boolean algebras. The original proof of Kelley used functional analytic techniques. We replace these techniques with Linear Programming and Tychonoff's theorem.

Aversa, V., Rao, K. 2002. Kelley's theorem from the duality of LP and Tychonoff's theorem. In Mathematica Slovaca, vol. 52, no.3, pp. 309-314. 0139-9918.

Aversa, V., Rao, K. (2002). Kelley's theorem from the duality of LP and Tychonoff's theorem. Mathematica Slovaca, 52(3), 309-314. 0139-9918.