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Invariant measures with values in locally convex spaces. (Spanish: Medidas invariantes con valores en espacios localmente convexos)

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Bombal Gordón, Fernando (1973) Invariant measures with values in locally convex spaces. (Spanish: Medidas invariantes con valores en espacios localmente convexos). In Actas de las primeras jornadas luso-españolas : celebradas en Lisboa durante los dias 4 al 8 de abril, 1972. Instituto Jorge Juan de Matemáticas, Madrid, pp. 148-154. ISBN 8400039483



Abstract

Let E be a locally compact space, and X a locally convex (real or complex) Hausdorff quasicomplete
vector space. Let μ0 be a positive Radon measure on E; corresponding to this measure
the author defines a certain measure μ on E with values on X. In the case in which E is a locally
compact topological group, and μ0 a left [right] Haar measure, μ is also a left [right] Haar measure.
Let T:X !X be a continuous linear mapping, and μ a left [right] Haar measure on E with values
on X; then T ·μ is also a left [right] Haar measure. Conversely, let μ be a left [right] Haar measure
on E with values on X, let be any left [right] Haar measure on E with values on X; the author
proves that = T · μ, where T:X ! X is a continuous linear mapping. This generalizes the
known theorem of H. Weyl on positive Haar measures.


Item Type:Book Section
Uncontrolled Keywords:Invariant measures;Haar measure.
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:17743
Deposited On:17 Jan 2013 09:02
Last Modified:25 Jan 2013 14:27

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