On extension theorems for M-measures in l-groups

Mathematica Slovaca

Volumn 60, Issue 1, 2010, Pages 65-74

  Boccuto, Antonio ^a   Riečan, Beloslav ^b  

^a UNIVERSITY OF PERUGIA   (Italy)

^b MATEJ BEL UNIVERSITY   (Slovakia)

Author keywords

Extension; L group; Weak distributivity

Indexed keywords

EID: 73449131881     PISSN: 01399918     EISSN: 13372211     Source Type: Journal    
DOI: 10.2478/s12175-009-0167-7     Document Type: Article

References (18)

1. ATANASSOV, K.: Intuitionistic Fuzzy Sets: Theory and Applications, Physics Verlag, New York, 1999.
2. S. J. Bernau 1965 Unique representation of Archimedean lattice groups and normal Archimedean lattice rings Proc. London Math. Soc. (3) 15 599 631 10.1112/plms/s3-15.1.599 182661
3. A. Boccuto 1995 On Stone-type extensions for group-valued measures Math. Slovaca 45 309 315 0857.28009 1361825
4. M. Duchoň B. Riečan 1996 On the Kurzweil-Stieltjes integral in ordered spaces Tatra Mt. Math. Publ. 8 133 141 0918.28013 1475272
5. D. H. Fremlin 1975 A direct proof of the Matthes-Wright integral extension theorem J. London Math. Soc. 11 3 276 284 0313.06016 10.1112/jlms/s2-11.3.276 380345
6. S. S. Khurana 1980 Extension of group-valued regular Borel measures Math. Nachr. 97 159 165 10.1002/mana.19800970113 600830
7. 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, pp. 18-24.
8. KUSRAEV, A. G.-MALYUGIN, S. A.: Some problems in the theory of vector measures, Akad. Nauk SSSR Sibirsk. Otdel., Inst. Mat., Novosibirsk, 1988 (Russian).
9. LUXEMBURG, W. A. J.-ZAANEN, A. C.: Riesz Spaces, I. North-Holland Math. Library, North-Holland Publishing Co., Amsterdam-London, 1971.
10. F. Maeda T. Ogasawara 1942 Representation of vector lattices J. Sci. Hiroshima Univ. Ser. A 12 17 35 0063.03704 29087
11. S. A. Malyugin 1991 Quasi-Radon measures Sibirsk. Mat. Zh. 32 101 111 1155807 [Translation: Siberian Math. J. 32 (1991), 812-821]
12. P. Mazureková B. Riečan 2006 A measure extension theorem Notes IFS 12 3 8
13. RIEČAN, B.: Probability theory on IF-events. In: A Volume in Honor of Daniele Mundici's 60th Birthday. Lect. Notes Comput. Sci. Eng., Springer, Berlin, 2007.
14. RIEČAN, B.-NEUBRUNN, T.: Integral, Measure and Ordering, Kluwer Academic Publishers/Ister Science, Dordrecht/Bratislava, 1997.
15. N. Shilkret 1971 Maxitive measure and integration Indag. Math. (N.S.) 33 109 116 288225
16. SIKORSKI, R.: Boolean Algebras, Springer-Verlag, Berlin-Göttingen- Heidelberg, 1960.
17. VULIKH, B. Z.: Introduction to the Theory of Partially Ordered Spaces, Wolters-Noordhoff Sci. Publ., Groningen, 1967.
18. J. D. M. Wright 1971 The measure extension problem for vector lattices Ann. Inst. Fourier (Grenoble) 21 65 85 0215.48101 330411