International Journal of Theoretical Physics

, Volume 3, Issue 5, pp 395–399 | Cite as

Probabilistic formulation of classical mechanics

  • N. S. Kronfli


Starting axiomatically with a system of finite degrees of freedom whose logicc is an atomic Boolean σ-algebra, we prove the existence of phase spaceΩc, as a separable metric space, and a natural (weak) topology on the set of statesI (all the probability measures onc) such thatΩc, the subspace of pure statesP, the set of atoms ofc and the spaceP(Ωc) of all the atomic measures on Ωc, are all homeomorphic. The only physically accessible states are the points ofΩc. This probabilistic formulation is shown to be reducible to a purely deterministic theory.


Field Theory Elementary Particle Quantum Field Theory Classical Mechanic Probabilistic Formulation 
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Copyright information

© Plenum Publishing Company Limited 1970

Authors and Affiliations

  • N. S. Kronfli
    • 1
  1. 1.Department of MathematicsBirkbeck CollegeLondon W.C.1

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