caa a22 4500 47574022X CHVBK 20180406123457.0 cr unu---uuuuu 170329e20000701xx s 000 0 eng 10.1007/BF02674650 doi (NATIONALLICENCE)springer-10.1007/BF02674650 Lyudkovskii S. Institute of General Physics, Russian Academy of Science, USSR aut Measurability of automorphisms of topological groups [Elektronische Daten] [S. Lyudkovskii] Relations between the measurability and continuity of algebraic automorphisms of topological groups depending on the types of groups are examined. Various cases are considered and theorems on the continuity of measurable automorphisms are proved; for instance, such theorems are proved for separable locally compact groups and automorphisms measurable with respect to nonnegative Haar measures. On the other hand, examples of nonmetrizable nonseparable compact groups with Haar measures and of non-locally-compact separable metrizable groups with measures μ quasi-invariant with respect to dense subgroups admittings μ-measurable discontinous automorphisms are given. Kluwer Academic/Plenum Publishers, 2000 Haar measure nationallicence quasi-invariant measure nationallicence continuous automorphism nationallicence discontinuous automorphism nationallicence measurable automorphism nationallicence locally compact groups nationallicence Mathematical Notes Nauka/Interperiodica 68/1(2000-07-01), 90-96 0001-4346 68:1<90 2000 68 11006 https://doi.org/10.1007/BF02674650 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02674650 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Lyudkovskii S. Institute of General Physics, Russian Academy of Science, USSR aut NATIONALLICENCE 773 0- Mathematical Notes Nauka/Interperiodica 68/1(2000-07-01), 90-96 0001-4346 68:1<90 2000 68 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer