**Abstract:**
This paper is devoted to the well known transformations that preserve a
large deviation principle (LDP), namely, the contraction principle with
approximately continuous maps and the concepts of exponential
equivalence and exponential approximations. We generalize these
transformations to completely regular topological state spaces, give
some examples and, as an illustration, reprove a generalization of
Sanov's theorem, due to de Acosta. Using partition-dependent couplings,
we then extend this version of Sanov's theorem to triangular arrays and
prove a full LDP for the empirical measures of exchangeable sequences with a
general measurable state space.

**Keywords:**
large deviations,
exponential equivalence,
contraction principle,
gauge space,
uniform space,
approximately continuous map,
triangular array,
exchangeable sequence

**2010
Mathematics Subject Classification:**

- 60F10 Large deviations
- 60G09 Exchangeability

**Reference:**
Stochastic
Processes and Their Applications, Vol. 77 (1998), No. 2, 139-154

DOI: 10.1016/S0304-4149(98)00047-7

**The paper (17 pages, revised version, May 26, 1998) is available in:**

- PDF / portable document format (259kB)

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