<sod>  
 The Borel measure is not [[complete measure|complete]], which is why in practice the complete [[Lebesgue measure]] is preferred: every Borel measurable set is also Lebesgue measurable, and the measures of the set agree.
 
In a more general (abstract) measure-theoretic context, Let E be a [[Hausdorff_space|Hausdorff space]].  A measure <math>\mu</math> is '''Borel''' iff <math>\mu(K) < +\infty\ \forall K \subset E</math> compact.
 
 [[de:Borel-Maß]]
 [[fr:Mesure de Borel]]
 <eod> <sod> 
 The Borel measure is not [[complete measure|complete]], which is why in practice the complete [[Lebesgue measure]] is preferred: every Borel measurable set is also Lebesgue measurable, and the measures of the set agree.
 
In a more general (abstract) measure-theoretic context, Let E be a [[Hausdorff_space|Hausdorff space]].  A measure &mu; on the &sigma;-algbera <math>\mathfrak{B}(E) </math> (the [[Borel_algebra|Borel &sigma;-algebra]] on E) is '''Borel''' iff <math>\mu(K) < +\infty\ \forall K \subset E</math> compact.
 
 [[de:Borel-Maß]]
 [[fr:Mesure de Borel]]
 <eod>