TITLE: What's the use of a complete measure?
QUESTION [46 upvotes]: A complete measure space is one in which any subset of a measure-zero set is measurable.
For what reasons would I want a complete measure space?  The only reason I can think of is in the context of probability theory: using complete probability spaces forces almost-everywhere equal random variables to generate the same sigma-sub-algebra.
Am I missing some other important technical reasons?

REPLY [4 votes]: Hi Tom E, 
Here is another reason: Let $E$ be a Borel set in Euclidean space. Then its image under a continuous map is always Lebesgue-measurable but in general not Borel measurable. Results like this make the completion useful; The theory behind this is the theory of analytic sets or the Souslin operation.