Stone-Weierstrass theorems for random functions
DOI:
https://doi.org/10.24193/subbmath.2019.2.10Keywords:
Stone-Weierstrass theorem, approximation of random functions, stochastic convergence, random polynomialAbstract
We present several generalizations ofStone-Weierstrass theorem about
the approximation of continuous functions
on a compact set by function from a subalgebra
to the case of random functions and random variables
in the space of continuous functions. The continuity
of the random functions is allowed to be only with
respect to a metric, hence including the case of
stochastically continuous random functions.
These results could be cornerstones of a general
approximation theory for random functions.
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Published
2019-06-12
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