Summary
In this paper are considered some conditions on locally compact topological groups that have arisen from the statistical analysis of group-invariant experiments and from probability theory. A catalogue is compiled of these conditions and of similar conditions that arise in the area of invariant means on locally compact topological groups. Known facts about the implication diagram of the conditions are described and some new implications are established. Counter-examples are discussed. An attempt is then made to throw some new light on the statistical relevance of the conditions in test theory, information theory and decision theory.
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Research partly supported by the Office of Naval Research while the first author was at the University of Wisconsin.
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Stone, M., von Randow, R. Statistically inspired conditions on the group structure of invariant experiments and their relationships with other conditions on locally compact topological groups. Z. Wahrscheinlichkeitstheorie verw Gebiete 10, 70–80 (1968). https://doi.org/10.1007/BF00572923
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DOI: https://doi.org/10.1007/BF00572923