%0 Book Section
%T Invariant measures with values in locally convex spaces. (Spanish: Medidas invariantes con valores en espacios localmente convexos)
publisher Instituto Jorge Juan de Matemáticas
%D 1973
%U 8400039483
%@ https://hdl.handle.net/20.500.14352/65429
%X Let E be a locally compact space, and X a locally convex (real or complex) Hausdorff quasicompletevector space. Let μ0 be a positive Radon measure on E; corresponding to this measurethe author defines a certain measure μ on E with values on X. In the case in which E is a locallycompact 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 valueson X; then T ·μ is also a left [right] Haar measure. Conversely, let μ be a left [right] Haar measureon E with values on X, let   be any left [right] Haar measure on E with values on X; the authorproves that   = T · μ, where T:X ! X is a continuous linear mapping. This generalizes theknown theorem of H. Weyl on positive Haar measures.
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