 The Borel measure agrees with the Lebesgue measure on those sets for which it is defined; however, there are many more Lebesgue-measurable sets than there are Borel measurable sets.The Borel measure is translation-invariant, but not complete.The Haar measure can be defined on any locally compact group and is a generalization of the Lebesgue measure (R"n" with addition is a locally compact group).