caa a22 4500 465825052 CHVBK 20180323112147.0 cr unu---uuuuu 170327e19900401xx s 000 0 eng 10.1007/BF01833150 doi (NATIONALLICENCE)springer-10.1007/BF01833150 Fuglede B. Mathematics Institute, University of Copenhagen, Universitetsparken 5, DK-2100, Copenhagen, Denmark aut On the mean value property of finely harmonic and finely hyperharmonic functions [Elektronische Daten] [B. Fuglede] Summary: It is shown that a finely superharmonic function in a planar fine domainU is greater than or equal to its lower integral with respect to harmonic measure associated with any bounded finely open setV with fine closure contained inU. Examples are given showing that this result does not extend to dimension 3 or more (unlessf is supposed to be, e.g., lower bounded onV) and also that the integral need not exist. Birkhäuser Verlag, 1990 Primary 31A99, 31B99 nationallicence aequationes mathematicae Birkhäuser-Verlag 39/2-3(1990-04-01), 198-203 0001-9054 39:2-3<198 1990 39 10 https://doi.org/10.1007/BF01833150 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01833150 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Fuglede B. Mathematics Institute, University of Copenhagen, Universitetsparken 5, DK-2100, Copenhagen, Denmark aut NATIONALLICENCE 773 0- aequationes mathematicae Birkhäuser-Verlag 39/2-3(1990-04-01), 198-203 0001-9054 39:2-3<198 1990 39 10 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer