Summary
Let (μ x) be a random measure on a measure space (Ω, Σ, μ), such that all μ x are diffuse measures. Then there is a subalgebra Σ 0⊂Σ with \(\mu _{|\Sigma _o }\)non-atomic such that \((\mu _{x|\Sigma _o } )\)is absolutely μ-continuous. This is applied to product measures and bounded linear operators on L 1(Ω,ν).
Article PDF
Similar content being viewed by others
References
Diestel, J., Uhl, J.: Vector measures, Mathematical surveys No. 15. Prov. R.I.: Amer. Math. Soc. 1977
Doss, R.: Convolution of singular measures. Studia Math. 45, 111–117 (1973)
Edgar, G.: Disintegration of measures and the vector-valued Radon-Nikodym theorem. Duke Math. J. 42, 447–450 (1975)
Kalton, N.J.: The Endomorphisms of L p(0≦p≦1). Indiana Univ. Math. J. 27, 353–381 (1978)
Lindenstrauß, J., Tzafriri, L.: Classical Banach Spaces II. Berlin-Heidelberg-New York: Springer 1979
Neveu, J.: Martingales à temps discret. Paris: Masson 1972
Talagrand, M.: Un théorème de théorie de la mesure lié à deux théorèmes de Mokobodzki. [To appear in Ann. Scient. Éc. Norm. Sup.]
Weis, L.: On the Representation of Order continuous operators by Random Measures. To appear in Trans. Amer. Math. Soc.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Weis, L. A note on diffuse random measures. Z. Wahrscheinlichkeitstheorie verw Gebiete 65, 239–244 (1983). https://doi.org/10.1007/BF00532481
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF00532481