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Thermal equilibrium by Gibbs and Poincaré. (Russian) Zbl 1143.82301
The author considers initial distributions of probability density $$\rho$$, which satisfy Liouville equation and are integrable with its square. Weak convergence of $$\rho$$ is formulated and the average value is defined according to the Birkhoff-Khinchine theorem as an integral of Hamilton equations. Weak convergence conditions are analyzed on the basis of Stone’s theorem via the Lebesgue-Stieltjes integral.

##### MSC:
 82B05 Classical equilibrium statistical mechanics (general) 80A10 Classical and relativistic thermodynamics