How is a Borel measure on Euclidean space defined?
I mean the Borel measure on the Borel sigma algebra generated by usual toplogy on an Euclidean space, which coincides with the normal definition of volume of subsets in the Euclidean space.
For Lebesgue measure on an Euclidean space, it is defined in terms of the outer measure on the power set of the Euclidean space.
If the Borel measure can be defined independent of the Lebesgue measure, then the Lebesgue measure can be defined in terms of the Borel measure by completion of measure. Right?
Thanks and regards!