Abstract
AbstractIn this paper, we study the Banach space $$\ell _{\infty }$$
ℓ
∞
of the bounded real sequences, and a measure $$N(a,\Gamma )$$
N
(
a
,
Γ
)
over $$\left( \textbf{R}^{\infty },\mathcal {B}^{\infty }\right) $$
R
∞
,
B
∞
analogous to the finite-dimensional Gaussian law. The main result of our paper is a change of variables’ formula for the integration, with respect to $$N(a,\Gamma )$$
N
(
a
,
Γ
)
, of the measurable real functions on $$\left( E_{\infty },\mathcal {B}^{\infty }\left( E_{\infty }\right) \right) $$
E
∞
,
B
∞
E
∞
, where $$E_{\infty }$$
E
∞
is the separable Banach space of the convergent real sequences. This change of variables is given by some $$\left( m,\sigma \right) $$
m
,
σ
functions, defined over a subset of $$E_{\infty }$$
E
∞
, with values on $$E_{\infty }$$
E
∞
, with properties that generalize the analogous ones of the finite-dimensional diffeomorphisms.
Funder
Università degli Studi di Trieste
Publisher
Springer Science and Business Media LLC
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