# Measures on complete metric spaces for which all meager sets are null

On a complete metric space the collection of meager and comeager sets form a $\sigma$-algebra. There is a 'natural' measure you can put on this $\sigma$-algebra where the measure of a meager set is 0 and the measure of every comeager set is some non-zero value such as 1 or $\infty$. When can such measures be extended to Borel, inner/outer regular, locally finite, and/or Radon measures? Can it be done in such a way that the only null sets are meager sets?