Editing Complete measure (section)

==Examples==
* [[Borel measure]] as defined on the Borel ''σ''-algebra generated by the [[Open set|open]] [[Interval (mathematics)|intervals]] of the real line is not complete, and so the above completion procedure must be used to define the complete Lebesgue measure. This is illustrated by the fact that the set of all Borel sets over the reals has the same cardinality as the reals. While the [[Cantor set]] is a Borel set, has measure zero, and its power set has cardinality strictly greater than that of the reals. Thus there is a subset of the Cantor set that is not contained in the Borel sets. Hence, the Borel measure is not complete.
* ''n''-dimensional Lebesgue measure is the completion of the ''n''-fold product of the one-dimensional Lebesgue space with itself. It is also the completion of the Borel measure, as in the one-dimensional case.