Minlos' theorem
Encyclopedia
In mathematics, Minlos' theorem states that a cylindrical measure on the dual of a nuclear space
is a Radon measure
if its Fourier transform
is continuous. It can be proved using Sazonov's theorem
.
Nuclear space
In mathematics, a nuclear space is a topological vector space with many of the good properties of finite-dimensional vector spaces. The topology on them can be defined by a family of seminorms whose unit balls decrease rapidly in size...
is a Radon measure
Radon measure
In mathematics , a Radon measure, named after Johann Radon, is a measure on the σ-algebra of Borel sets of a Hausdorff topological space X that is locally finite and inner regular.-Motivation:...
if its Fourier transform
Fourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...
is continuous. It can be proved using Sazonov's theorem
Sazonov's theorem
In mathematics, Sazonov's theorem, named after Vyacheslav Vasilievich Sazonov , is a theorem in functional analysis.It states that a bounded linear operator between two Hilbert spaces is γ-radonifying if it is Hilbert–Schmidt...
.