“Measure algebra”的意思、由来-开放百科全书

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Measure algebra

释义

Definition
References

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

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(Σx_i) = Σm(x_i) if the x_i are a countable set of elements that are disjoint (x_i ∧ x_j=0 whenever i≠j).

References

{{Citation | last1=Jech | first1=Thomas | author1-link=Thomas Jech | title=Set Theory | publisher=Springer-Verlag | location=Berlin, New York | edition=third millennium | series=Springer Monographs in Mathematics | isbn=978-3-540-44085-7 | doi=10.1007/3-540-44761-X_22 | year=2003| chapter=Saturated ideals|page=415}}

1 : Measure theory

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