Upper porosity with respect to measures (Q416430)

Let \(X\) be a separable metric space and \(\mu\) a Borel regular probability measure on \(X\). The author defines the notion of \(\mu\)-upper porosity for subsets of \(X\), thus generalizing the concept of upper porosity of \(\mu\) introduced by \textit{M. E. Mera} and \textit{M. Morán} [Real Anal. Exch. 26, No. 1, 101--115 (2001; Zbl 1023.28002)].NEWLINENEWLINEMore general types of \(\mu\)-upper porosity with respect to suitable porosity functions are explored. Finally, using ideas and results from [\textit{M. E. Mera, M. Morán, D. Preiss} and \textit{L. Zajíček}, Nonlinearity 16, No. 1, 247--255 (2003; Zbl 1026.28001)], several decomposition theorems for \(\mu\)-upper porous sets are proved.