caa a22 4500 445836318 CHVBK 20180317145331.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s00209-009-0615-7 doi (NATIONALLICENCE)springer-10.1007/s00209-009-0615-7 Moreno J. Dpto. Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049, Madrid, Spain aut Porosity and unique completion in strictly convex spaces [Elektronische Daten] [J. Moreno] We are concerned in this paper with topological and stochastic properties of the family $${\mathcal G}$$ of all closed convex sets with a unique extension to a complete set. With the help of a strengthened version of a lemma by Groemer we show that, in Minkowski spaces with a strictly convex norm, $${\mathcal G}$$ is lower porous. This improves a previous result from Groemer (Geom. Dedicata 20:319-334, 1986) where, in the same context, $${\mathcal G}$$ was proved to be nowhere dense. In contrast to this fact we show that, in these spaces, there is a stochastic construction procedure which provides a complete set with probability one. This generalizes an earlier result of Bavaud (Trans. Amer. Math. Soc. 333(1):315-324, 1992) proved for the particular case of the Euclidean plane. Springer-Verlag, 2009 Mathematische Zeitschrift Springer-Verlag 267/1-2(2011-02-01), 173-184 0025-5874 267:1-2<173 2011 267 209 https://doi.org/10.1007/s00209-009-0615-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-009-0615-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Moreno J. Dpto. Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049, Madrid, Spain aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 267/1-2(2011-02-01), 173-184 0025-5874 267:1-2<173 2011 267 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer