Review: K. R. Parthasarathy, Probability Measures on Metric Spaces
نویسندگان
چکیده
منابع مشابه
Probability Measures and Milyutin Maps between Metric Spaces
We prove that the functor P̂ of Radon probability measures transforms any open map between completely metrizable spaces into a soft map. This result is applied to establish some properties of Milyutin maps between completely metrizable space.
متن کاملTesting to distinguish measures on metric spaces
We study the problem of distinguishing between two distributions on a metric space; i.e., given metric measure spaces (X, d, μ1) and (X, d, μ2), we are interested in the problem of determining from finite data whether or not μ1 is μ2. The key is to use pairwise distances between observations and, employing a reconstruction theorem of Gromov, we can perform such a test using a two sample Kolmogo...
متن کاملRegular Variation for Measures on Metric Spaces
The foundations of regular variation for Borel measures on a complete separable space S, that is closed under multiplication by nonnegative real numbers, is reviewed. For such measures an appropriate notion of convergence is presented and the basic results such as a Portmanteau theorem, a mapping theorem and a characterization of relative compactness are derived. Regular variation is defined in...
متن کاملCoherent Risk Measures on General Probability Spaces
We extend the definition of coherent risk measures, as introduced by Artzner, Delbaen, Eber and Heath, to general probability spaces and we show how to define such measures on the space of all random variables. We also give examples that relates the theory of coherent risk measures to game theory and to distorted probability measures. The mathematics are based on the characterisation of closed ...
متن کاملComposition of Probability Measures on Finite Spaces
Decomposable models and Bayesian net works can be defined as sequences of oligo dimensional probability measures connected with opemtors of composition. The prelim inary results suggest that the probabilistic models allowing for effective computational procedures are represented by sequences pos sessing a special property; we shall call them perfect sequences. The present paper lays down th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Mathematical Statistics
سال: 1969
ISSN: 0003-4851
DOI: 10.1214/aoms/1177697834