Abstract
One of the powerful tools for study of topological groups and their representations is invariant means. Let L be an arbitrary linear topological space consisting of functions on a G-space X and invariant under translations. An invariant mean is a positive1 linear functional on L that is invariant under action of the group G. The most important case is that in which X is a topological group and G is the group of left, right, or two-sided translations on X. The corresponding means are also called left, right, or two-sided.
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© 1976 Springer-Verlag Berlin Heidelberg
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Kirillov, A.A. (1976). Invariant Integration. In: Elements of the Theory of Representations. Grundlehren der mathematischen Wissenschaften, vol 220. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-66243-0_9
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DOI: https://doi.org/10.1007/978-3-642-66243-0_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-66245-4
Online ISBN: 978-3-642-66243-0
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