Showing papers on "Gaussian measure published in 1974"

Absolute Continuity of Measures

Abstract: Absolute continuity and singularity play a very important role in the study of measures in infinite-dimensional spaces, for example, Hubert space. Although there can be no theory treating such questions for finite-dimensional spaces which of great interest, such a theory for infinite-dimensional spaces is possible. It contains such topics as the investigation of the absolute continuity and singularity of various concrete classes of measures, the finding of general conditions for absolute continuity or singularity in terms of finite-dimensional distributions, and other characteristics defining the measures. An important problem is the calculation of the density of a measure w.r.t. another when the measures are absolutely continuous and the determination of the non-overlapping sets on which singular measures are concentrated.

Einige Bemerkungen zu den Gauss-Verteilungen auf lokalkompakten abelschen Gruppen

Abstract: Let G be a connected locally compact abelian group and ν a symmetric Gaussian measure on G. We are concerned with the support of the measure ν and with the relation of ν to the Haar measure ω on G. It is shown that the support of ν is always a closed connected subgroup of G. On G there exists an absolutely continuous Gaussian measure (with respect to ω) if and only if G is locally connected and has a countable basis for its open sets. Special interest is given to Gaussian measures on toroidal groups.