probability measures on Polish spaces is investigated in a thorough and comprehensive way. As a special feature, no additional assumptions on the probability space in the background, such as completeness or a countable generated algebra, are made. One of the main results is a direct proof of the random analog of the Prohorov theorem, which is obtained without invoking an embedding of the Polish space into a compact space. Further, the narrow topology is examined and other natural topologies on random measures are compared. In addition, it is shown that the topology of convergence in law-which
relates to the ""statistical equilibrium""-and the narrow topology are incompatible. A brief section on random sets on Polish spaces provides the fundamentals of this theory. In a final section, the results are applied to random dynamical systems to obtain existence results for invariant measures on compact random sets, as well as uniformity results in the individual ergodic theorem. This clear and incisive volume is useful for graduate students and researchers in mathematical
analysis and its applications."
By:
Hans Crauel Imprint: CRC Press Country of Publication: United Kingdom Volume: v.11 Dimensions:
Height: 234mm,
Width: 156mm,
Spine: 13mm
Weight: 331g ISBN:9780415273879 ISBN 10: 0415273870 Pages: 136 Publication Date:25 July 2002 Audience:
Professional and scholarly
,
Professional and scholarly
,
Professional & Vocational
,
Undergraduate
,
Further / Higher Education
Format:Hardback Publisher's Status: Active
Notations and Some Technical Results. Random Sets. Random Probability Measures and the Narrow Topology. Prohorov Theory for Random Probability Measures. Further Topologies on Random Measures. Invariant Measures and Some Ergodic theory for Random Dynamical Systems A. The Narrow Topology on Non-Random Measures B. Scattered Results. Bibliography. Index.
