Publication: Invariant measures with values in locally convex spaces. (Spanish: Medidas invariantes con valores en espacios localmente convexos)
No Thumbnail Available
Official URL
Full text at PDC
Publication Date
1973
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Instituto Jorge Juan de Matemáticas
Citations
Exportar
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.