Balayages on Excessive Measures, their Representation and the Quasi-Lindelöf Property
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Tóm tắt
If Exc is the set of all excessive measures associated with a submarkovian resolvent on a Lusin measurable space and B is a balayage on Exc then we show that for any m∈Exc there exists a basic set A (determined up to a m-polar set) such that Bξ=(BA)*ξ for any ξ∈ Exc, ξ ≪ m. The m-quasi-Lindelöf property (for the fine topology) holds iff for any B there exists the smallest basic set A as above. We characterize the case when any B is representable i.e. there exists a basic set such that B=(BA)* on Exc.
Tài liệu tham khảo
Ben Saad, H. and Janßen, K.: ‘Topologie fine et mesure de référence’, J. Reine Angew. Math. 360(1985), 153-159.
Beznea, L. and Boboc, N.: ‘Absorbent, parabolic, elliptic and quasi-elliptic balayages in potential theory’, Rev. Roumaine Math. Pures Appl. 38(1993), 197-234.
Beznea, L. and Boboc, N.: ‘Duality and biduality for excessive measures’, Rev. Roumaine Math. Pures Appl. 39(1994), 419-438.
Beznea, L. and Boboc, N.: ‘Excessive functions and excessive measures: Hunt's theorem on balayages, quasi-continuity’, in Proc. Workshop on Classical and Modern Potential Theory and Applications, NATO ASI Series C 430, pp. 77-92. Kluwer, 1994.
Beznea, L. and Boboc, N.: ‘On the integral representation for excessive measures’, Rev. Roumaine Math. Pures Appl. 40(1995), 725-734.
Beznea, L. and Boboc, N.: ‘Once more about the semipolar sets and regular excessive functions’, in Potential Theory - ICPT 94, pp. 255-274. de Gruyter, 1996.
Beznea, L. and Boboc, N.: ‘Quasi-boundedness and subtractivity; applications to excessive measures’, Potential Analysis 5(1996), 467-485.
Boboc, N., Bucur, Gh. and Cornea, A.: Order and Convexity in Potential Theory: H-Cones, Lecture Notes in Math. 853, Springer, 1981.
Dellacherie, C. and Meyer, P. A.: Probabilités et Potentiel, Ch I-IV, IX-XI, XII-XVI, Hermann, 1975, 1983, 1987.
Doob J. L.: ‘Applications to analysis of a topological definition of smallness of a set’, Bull. Amer. Math. Soc. 72(1966), 579-600.
Feyel, D.: ‘Ensembles singuliers associés aux espaces de Banach ré ticulés’, Ann. Inst. Fourier, Grenoble 31(1981), 193-223.
Feyel, D.: ‘Sur la théorie fine du potentiel’, Bull. Soc. Math. France 111(1983), 41-57.
Fitzsimmons, P. J.: ‘Homogeneous random measures and weak order for excessive measures of a Markov process’, Trans. Amer. Math. Soc. 303(1987), 431-478.
Fitzsimmons, P. J. and Getoor, R. K.: ‘A weak quasi-Lindelöf property and quasi-fine support of measures’, Math. Ann. 301(1995), 751-762.
Fitzsimmons, P. J. and Maisonneuve B.: ‘Excessive measures and Markov processes with random birth and death’, Probab. Th. Rel. Fields 72(1986), 319-336.
Getoor, R. K.: Excessive Measures, Birkhäuser, Boston, 1990.
Mokobodzki, G.: ‘Pseudo-quotient de deux mesures, application à la dualité’, in Séminaire de probabilités VII, Lecture Notes in Math. 321, 318-321, Springer, 1973.
Sharpe, M. J.: General Theory of Markov Processes, Academic Press, 1988.
Steffens, J.: ‘Duality and integral representation for excessive measures’, Math. Z. 210(1992), 495-512.
Walsh, J. and Winkler, W.: ‘Absolute continuity and the fine topology’, in Seminar on Stochastic Processes, pp. 151-157, Birkhäuser, 1981.