λ加性测度的一般poincar公式的初等证明

Acta Cybern. Pub Date : 2019-11-03 DOI:10.14232/actacyb.24.2.2019.1

J. Dombi, T. Jónás

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引用次数: 2

摘要

在我们之前的一篇论文[4]中，我们给出了n集并集的λ加性测度的一般公式，并给出了证明。这个证明是基于加性测度是可表示的这一事实。本文给出了n集并集的加性测度公式的一个新颖的初等证明。本文还利用初等技术证明了概率论中著名的庞加莱公式只是我们一般公式的一个极限情况。

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

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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来源期刊

Acta Cybern.

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