It is shown that for any KMS-state of a classical system of noncoincident particles, the distribution functions are absolutely continuous with respect to Lebesgue measure; the equivalence between KMS states and Canonical Gibbs States is then established.

A generalised integration by parts formula for sequences of absolutely continuous functions that satisfy the w−Appell condition and different estimates for the remainder are provided. Applications for particular instances of such sequences are pointed out as well.

In this paper we characterize possible asymptotics for hitting times in aperiodic ergodic dynamical systems: asymptotics are proved to be the distribution functions of subprobability measures on the line belonging to the functional class (A) F = F is continuous and concave; F (t) ≤ t for t ≥ 0.. Note that all possible asymptotics are absolutely continuous.

We formally state and prove the wellposedness and the local Lipschitz continuity of the multisurface stress-strain law of nonlinear kinematic hardening type due to Chaboche within the space of time-dependent tensor-valued absolutely continuous functions. The results also include the more general case of a continuous family of auxiliary surfaces.