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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
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