caa a22 4500 605509050 CHVBK 20210128100639.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s00010-015-0353-3 doi (NATIONALLICENCE)springer-10.1007/s00010-015-0353-3 Járai Antal Eötvös Loránd University Budapest, Pázmány Péter sétány 1/D, 1117, Budapest, Hungary aut Regularity properties of measurable functions satisfying a multiplicative type functional equation almost everywhere [Elektronische Daten] [Antal Járai] For functional equations originating from probability theory the equation is satisfied for the density functions only almost everywhere by the nature of the method used to obtain it. There are standard theorems proving that all measurable solutions can be extended uniquely to continuous solutions, but in some cases—for example, for multiplicative equations—these can be applied only if we also prove that the solutions are nonzero, too. We shall consider such an example and prove a general theorem as well. Springer Basel, 2015 Aequationes mathematicae Springer Basel 89/2(2015-04-01), 367-381 0001-9054 89:2<367 2015 89 10 https://doi.org/10.1007/s00010-015-0353-3 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00010-015-0353-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Járai Antal Eötvös Loránd University Budapest, Pázmány Péter sétány 1/D, 1117, Budapest, Hungary aut NATIONALLICENCE 773 0- Aequationes mathematicae Springer Basel 89/2(2015-04-01), 367-381 0001-9054 89:2<367 2015 89 10