An elementary proof of the general Poincaré formula for λ-additive measures
In a previous paper of ours (see J. Dombi and T. J´on´as. The general Poincaré formula for λ-additive measures. Information Sciences, 490:285-291, 2019.), we presented the general formula for λ-additive measure of union of n sets and gave a proof of it. That proof is based on the fact that the λ-add...
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| Main Authors: | |
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| Format: | Article |
| Published: |
2019
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| Series: | Acta cybernetica
24 No. 2 |
| Kulcsszavak: | Henri Poincaré, Matematika |
| Subjects: | |
| doi: | 10.14232/actacyb.24.2.2019.1 |
| Online Access: | http://acta.bibl.u-szeged.hu/64707 |
| Summary: | In a previous paper of ours (see J. Dombi and T. J´on´as. The general Poincaré formula for λ-additive measures. Information Sciences, 490:285-291, 2019.), we presented the general formula for λ-additive measure of union of n sets and gave a proof of it. That proof is based on the fact that the λ-additive measure is representable. In this study, a novel and elementary proof of the formula for λ-additive measure of the union of n sets is presented. Here, it is also demonstrated that, using elementary techniques, the well-known Poincar´e formula of probability theory is just a limit case of our general formula. |
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| Physical Description: | 173-185 |
| ISSN: | 0324-721X |