### A Well Behaved Quasi-distance for Spaces of Homogeneous Type

#### Abstract

For any space of homogeneous type a quasi-distance equivalent to the original one is obtained satisfying that, if B and B' are balls such the center of the B' belongs to B and the radius of B' is smaller than the radius of B then, the measure of the intersection of B and B' is smaller than a constant fraction of the measure of the B'. An application to weighted norm inequalities for Hardy-Littlewood maximal function, which extends a result of A. P. Calderón, is given.