An extension result for continuous valuations

Journal of the London Mathematical Society

Volumn 61, Issue 2, 2000, Pages 629-640

  Alvarez Manilla, M ^a   Edalat, A ^a   Saheb Djahromi, N ^b  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b UNIVERSITÉ BORDEAUX 1   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038413211     PISSN: 00246107     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0024610700008681     Document Type: Article

References (26)

1. S. ABRAMSKY and A. JUNG, 'Domain theory', Handbook of logic in computer science - Vol. 3 (ed. D. M. Gabbay, S. Abramsky and T. S. E. Maibaum, Oxford University Press, 1994) 1-168.
2. M. ALVAREZ-MANILLA, A. EDALAT and N. SAHEB-DJAHROMI, 'An extension result for continuous valuations' Electronic notes in theoretical computer science - Vol. 13 (Elsevier, 1998) http://www.elsevier.nl/locate/entcs/volume13.html (extended abstract).
3. P. BILLINGSLEY, Ergodic theory and information (Robert E. Krieger Publishing, Huntington, New York, 1965).
4. G. BIRKHOFF, Lattice theory, 3rd edn (American Mathematical Society, Providence, RI, 1967).
5. R. M. DUDLEY, Real analysis and probability (Wadsworth & Brooks/Cole, 1989).
6. A. EDALAT, 'Domain theory and integration', Theoret. Comput. Sci. 151 (1995) 163-193.
7. A. EDALAT, 'Domains for computation in mathematics, physics and exact real arithmetic', Bull. Symbolic Logic 3 (1997) 401-452.
8. G. GIERZ, K. H. HOFMANN, K. KEIMEL, J. D. LAWSON, M. MISLOVE and D. S. SCOTT, A compendium of continuous lattices (Springer, Berlin, 1980).
9. P. R. HALMOS, Measure theory (Van Nostrand, Princeton, NJ, 1950).
10. R. HECKMANN, 'Spaces of valuations', Papers on general topology and applications. Eleventh Summer Conference at the university of Southern Maine, Annals of the New York Academy of Sciences 806 (ed. S. Andima, R. C. Flagg, G. Itzkowitz, Y. Kong, R. Kopperman and P. Misra, New York Academy of Sciences, New York, 1996).
11. A. HORN and A. TARSKI, 'Measures in Boolean algebras', Trans. Amer. Math. Soc. 64 (1948) 467-497.
12. P. JOHNSTONE, Stone spaces (Cambridge University Press, 1982).
13. C. JONES, 'Probabilistic non-determinism', PhD thesis, University of Edinburgh, 1989.
14. C. JONES and G. PLOTKIN, 'A probabilistic powerdomain of evaluations', IEE Symposium on Logic in Computer Science '89 (IEEE Computer Society Press, Silver Spring, MD, 1989) 186-195.
15. T. KAMAE, U. KRENGEL and G. L. O'BRIEN, 'Stochastic inequalities on partially ordered spaces', Ann. Probab. 5 (1977) 899-912.
16. J. D. LAWSON, 'Valuations in continuous lattices', Continuous lattices and related topics, Mathematik Arbeitspapiere 27 (ed. R. E. Hoffmann, Universität Bremen, 1982).
17. M. LOÈVE, 'On almost sure convergence', Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, 1951) 279-303.
18. S. W. NASH, 'An extension of the Borel-Cantelli Lemma', Ann. of Math. Statistics 25 (1954) 165-168.
19. T. NORBERG, 'Existence theorems for measures on continuous posets, with applications to random set theory', Math. Scand. 64 (1989) 15-51.
20. T. NORBERG and W. VERVAAT, 'Capacities on non-Hausdorff spaces', Probability and lattices, CWI Tracts 110 (ed. W. Vervaat and H. Holwerda, SMC, Centrum voor Wiskunde en Informatica, Amsterdam, 1997).
21. B. J. PETTIS, 'On the extension of measures', Ann. of Math. 54 (1951) 186-197.
22. H. L. ROYDEN, Real analysis, 3rd edn (Macmillan, New York, 1988).
23. N. SAHEB-DJAHROMI, 'Cpo's of measures for nondeterminism', Theoret. Comput. Sci. 12 (1980) 19-37.
24. M. F. SMILEY, 'An extension of metric distributive lattices with an application in general analysis', Trans. Amer. Math. Soc. 56 (1944) 435-447.
25. V. STRASSEN, 'The existence of probability measures with given marginals', Ann. of Math. Statistics 36 (1965) 423-439.
26. R. TIX, 'Stetige Bewertungen auf topologischen Räumen', Master's thesis, Technische Hochschule Darmstadt, 1995.