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An Elementary Approach to the Daniell‐Kolmogorov Theorem and Some Related Results
Author(s) -
Kallenberg Olav
Publication year - 1988
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19881390123
Subject(s) - mathematics , unit interval , lebesgue measure , probability measure , elementary proof , lebesgue integration , interval (graph theory) , measure (data warehouse) , product measure , conditional expectation , standard probability space , discrete mathematics , conditional probability , conditional probability distribution , product (mathematics) , pure mathematics , combinatorics , statistics , geometry , database , computer science
Abstract We give a short elementary proof of the Daniell‐Kolmogorov existence theorem for probability measures on product spaces, assuming nothing but the existence of Lebesgue measure on the unit interval. Related approaches are used to prove the existence of regular conditional distributions directly on Polish spaces, and to establish the existence of random measures and sets with given finite‐dimensional distributions or hitting probabilities, respectively.