Spectral potential, Kullback action, and large deviation principlefor finitely-additive measures

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.