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Standard H-cones and balayage spaces

IV Section — Potential Theory

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1014)

Abstract

In this paper we study the relations between standard H-cones (c.f.[2],[3] and [4]) and balayage spaces (c.f.[1]). It turns out, that a standard H-cone S is associated with a balayage space if and only if S can be represented on a Bauer-simplex (i.e. a Choquet-simplex for which the set of extreme points is closed).

Keywords

  • Extreme Point
  • Radon Measure
  • Natural Topology
  • Continuous Element
  • Martin Boundary

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Bibliography

  1. Bliedtner, J., Hansen, W.: Markov Processes and Harmonic Spaces. Z.Wahrscheinlichkeitstheorie verw. Gebiete 42 309–325 (1978)

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  2. Boboc, N., Bucur, Gh., Cornea, A.: H-Cones and Potential Theory. Ann.Inst.Fourier 25, 71–108 (1975)

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  3. Boboc, N., Cornea, A.: Cônes convexes ordonnés. H-cônes et adjoints de H-cônes. C.R.Acad.Sci.Paris 270, 596–599 (1970)

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  4. Boboc, N., Bucur, Gh., Cornea, A., Höllein, H.: Order and Convexity in Potential Theory: H-Cones. Lecture Notes in Math.853.Berlin-Heidelberg-New York: Springer (1981)

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  5. Dembinski, V., Janßen, K.: Standard Balayage Spaces and Standard Markov Processes. Lecture Notes in Math.787, 84–105. Berlin-Heidelberg-New York: Springer (1980)

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  6. Helms, L.L.: Introduction to Potential Theory. New York-London-Sydney-Toronto: Wiley (1969).

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© 1983 Springer-Verlag

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Janßen, K. (1983). Standard H-cones and balayage spaces. In: Cazacu, C.A., Boboc, N., Jurchescu, M., Suciu, I. (eds) Complex Analysis — Fifth Romanian-Finnish Seminar. Lecture Notes in Mathematics, vol 1014. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072079

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  • DOI: https://doi.org/10.1007/BFb0072079

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12683-6

  • Online ISBN: 978-3-540-38672-8

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