@article{ECP1370,
author = {Henri Comman},
title = {Stone-Weierstrass type theorems for large deviations},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {13},
year = {2008},
keywords = {Large deviations, rate function, Bryc's theorem},
abstract = {We give a general version of Bryc's theorem valid on any topological space and with any algebra $\mathcal{A}$ of real-valued continuous functions separating the points, or any well-separating class. In absence of exponential tightness, and when the underlying space is locally compact regular and $\mathcal{A}$ constituted by functions vanishing at infinity, we give a sufficient condition on the functional $\Lambda(\cdot)_{\mid \mathcal{A}}$ to get large deviations with not necessarily tight rate function. We obtain the general variational form of any rate function on a completely regular space; when either exponential tightness holds or the space is locally compact Hausdorff, we get it in terms of any algebra as above. Prohorov-type theorems are generalized to any space, and when it is locally compact regular the exponential tightness can be replaced by a (strictly weaker) condition on $\Lambda(\cdot)_{\mid \mathcal{A}}$.},
pages = {no. 22, 225-240},
issn = {1083-589X},
doi = {10.1214/ECP.v13-1370},
url = {http://ecp.ejpecp.org/article/view/1370}}