Upper porous measures on metric spaces
The porosity of a measure at a point on a metric space indicates how large, as measured by radius, balls of relatively small measure can be relative to balls centered at the point in question. Proper formulations, too lengthy to reproduce here, involve limits of suprema of numbers with the right property. The author is concerned with a variation called upper porosity and gives a technical sufficient condition for a measure to be upper porous. In Euclidean spaces upper porosity is equivalent to having lower conical density zero at almost all points. The paper closed with an example of a Hausdorff measure on \([0,1]\) that is not upper porous.
scientific article; zbMATH DE number 5615679
scientific article