Geodesic
Spectral potential, Kullback action, and large deviation principlefor finitely-additive measures
Trudy Instituta matematiki, Tome 23 (2015) no. 2, pp. 11-23

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The known large deviation principle for empirical measures, generated by a sequence if i.i.d. random variables, is extended to the case of finitely-additive and nonnormalized distributions. For the Kullback–Leibler information function we prove a least action principle and gauge identities, linking the Kullback–Leibler information function with its Legendre dual functional. 
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     title = {Spectral potential, {Kullback} action, and large deviation principlefor finitely-additive measures},
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V. I. Bakhtin. Spectral potential, Kullback action, and large deviation principlefor finitely-additive measures. Trudy Instituta matematiki, Tome 23 (2015) no. 2, pp. 11-23. http://geodesic.mathdoc.fr/item/TIMB_2015_23_2_a1/