In the
mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
of
topological vector space
In mathematics, a topological vector space (also called a linear topological space and commonly abbreviated TVS or t.v.s.) is one of the basic structures investigated in functional analysis.
A topological vector space is a vector space that is als ...
s, Minlos's theorem states that a
cylindrical measure on the dual of a
nuclear space
In mathematics, nuclear spaces are topological vector spaces that can be viewed as a generalization of finite-dimensional Euclidean spaces and share many of their desirable properties. Nuclear spaces are however quite different from Hilbert spaces, ...
is a
Radon measure
In mathematics (specifically in measure theory), a Radon measure, named after Johann Radon, is a measure on the -algebra of Borel sets of a Hausdorff topological space that is finite on all compact sets, outer regular on all Borel sets, and ...
if its
Fourier transform
In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the tr ...
is continuous. It is named after
Robert Adol'fovich Minlos and can be proved using
Sazonov's theorem.
References
*
*
Theorems in functional analysis
Theorems about stochastic processes
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