A measure algebra is a Boolean algebra B with a measure m, which is a real-valued function on B such that:
m(0)=0, m(1)=1
m(x) >0 if x≠0
m is countably additive: m(Σxi) = Σm(xi) if the xi are a countable set of elements that are disjoint (xi ∧ xj=0 whenever i≠j).
Referencesedit
Jech, Thomas (2003), "Saturated ideals", Set Theory, Springer Monographs in Mathematics (third millennium ed.), Berlin, New York: Springer-Verlag, p. 415, doi:10.1007/3-540-44761-X_22, ISBN978-3-540-44085-7
December 17, 2023
measure, algebra, mathematics, measure, algebra, boolean, algebra, with, countably, additive, positive, measure, probability, measure, measure, space, gives, measure, algebra, boolean, algebra, measurable, sets, modulo, null, sets, definition, edita, measure, . In mathematics a measure algebra is a Boolean algebra with a countably additive positive measure A probability measure on a measure space gives a measure algebra on the Boolean algebra of measurable sets modulo null sets Definition editA measure algebra is a Boolean algebra B with a measure m which is a real valued function on B such that m 0 0 m 1 1 m x gt 0 if x 0 m is countably additive m Sxi Sm xi if the xi are a countable set of elements that are disjoint xi xj 0 whenever i j References editJech Thomas 2003 Saturated ideals Set Theory Springer Monographs in Mathematics third millennium ed Berlin New York Springer Verlag p 415 doi 10 1007 3 540 44761 X 22 ISBN 978 3 540 44085 7 Retrieved from https en wikipedia org w index php title Measure algebra amp oldid 761714739, wikipedia, wiki, book, books, library,
