An Elementary Proof of the General Poincaré Formula for λ-additive Measures

József Dombi; Tamás Jónás

doi:10.14232/actacyb.24.2.2019.1

József Dombi Department of Computer Algorithms and Artificial Intelligence, University of Szeged
Tamás Jónás Institute of Business Economics, Eötvös Loránd University

DOI: https://doi.org/10.14232/actacyb.24.2.2019.1

Keywords: λ-additive measure, Poincaré formula

Abstract

In a previous paper of ours [4], we presented the general formula for lambda-additive measure of union of n sets and gave a proof of it. That proof is based on the fact that the lambda-additive measure is representable. In this study, a novel and elementary proof of the formula for lambda-additive measure of the union of n sets is presented. Here, it is also demonstrated that, using elementary techniques, the well-known Poincare formula of probability theory is just a limit case of our general formula.

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