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Level Sets and the Uniqueness of Measures
Author(s) -
Alspach Dale E.
Publication year - 1993
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-48.2.249
Subject(s) - uniqueness , range (aeronautics) , property (philosophy) , mathematics , interval (graph theory) , measure (data warehouse) , finite set , pure mathematics , mathematical analysis , combinatorics , computer science , data mining , engineering , aerospace engineering , philosophy , epistemology
A result of Nymann is extended to show that a positive σ‐finite measure with range an interval is determined by its level sets. An example is given of two finite positive measures with range the same finite union of intervals but with the property that one is determined by its level sets and the other is not.