In the
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
of
topological vector spaces, Minlos's theorem states that a
cylindrical measure In mathematics, cylinder set measure (or promeasure, or premeasure, or quasi-measure, or CSM) is a kind of prototype for a Measure (mathematics), measure on an infinite-dimensional vector space. An example is the Gaussian cylinder set measure on Hil ...
on the dual of a
nuclear space is a
Radon measure if its
Fourier transform
A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...
is continuous. It is named after
Robert Adol'fovich Minlos and can be proved using
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 a Hilbert–Schmidt o ...
.
References
*
*
Theorems in functional analysis
Theorems regarding stochastic processes
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