16-17 May 2019 • Sofia, Bulgaria

Submission: 21 February 2019Notification: 11 March 2019Final Version: 1 April 2019

Issue:A measure extension theorem

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Title of paper: A measure extension theorem
Author(s):
Beloslav Riečan
Faculty of Natural Sciences, Matej Bel University, Tajovského 40, SK-974 01 Banská Bystrica
Mathematical Institute of Slovak Acad. of Sciences, Štefánikova 49, SK-81473 Bratislava
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Petra Mazureková
Faculty of Natural Sciences, Matej Bel University, Tajovského 40, SK-974 01 Banská Bystrica
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Presented at: 2nd International Workshop on Intuitionistic Fuzzy Sets, 3 December 2006, Banská Bystrica, Slovakia.
Published in: Proceedings, published in Notes on Intuitionistic Fuzzy Sets, Volume 12, Number 4, pages 3—8
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Abstract: In the paper continuous set functions are considered where the additional condition is substituted by max-min condition: μ(A⋃B) = max(μ(A), μ(B)), μ(A⋂B) = min(μ(A), μ(B)). For such functions the extension theorem is proved from an algebra to the generalized σ-algebra.


References:
  1. Krachounov, M.: Intuitionistic probability and intuitionistic fuzzy sets. In: First International Workshop on Intuitionistic Fuzzy Sets, Generalized Nets and Knowledge Engeneering (E. El-Darzi. R. Atanassov, P. Chountas eds.) Univ. of Westminister, London 2006, 18-24.
  2. Pap, E.: Pseudoadditive measures and their applications. In: Handbook of Measure Theory (E. Pap ed.). Elsevier, Amsterdam 2002, 1403 - 1465.
  3. Riečanová, Z.: About δ-additive and δ-maxitive measures. Math. Slovaca 32, 1982, 413 -436.
  4. Shilkret, N.: Maxitive measure and integration. Indag.Math. 33 (1971), 109 - 116.
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