The Boltzmann Distribution through a Maximum Entropy Principle

The maximum-entroy distribution is derived for the Wienr-Shannon entropy for absolutely continuous distributions when the mean value of a function in a suitable class is prescribed. Three cases are studied, according as to whether the distribution has support in a closed interval, on the non-negative half line or on the real line

Orlicz Metrics Derive from a Single Probabilistic Metric

It is shown that the same probabilistic metric as used by Schweizer and Sklar to obtain all $L^p$ space metrics can be used to drive the metrics of Orlicz spaces

Sopra alcune proprietà dell'entropia dipendente dall'errore

Si studiano alcune proprietà dell'entrpia dipendente dall'errore; allo scopo si introducono alcune operazioni sullo spazio delle funzioni di ripartizione

Product Topologies on the Space of Distribution Functions

We study the connection between weak convergence in the space $\Delta_r$ of multiple distribution functions and convergence in the product topology induced on the product $\Delta\times\dots\times\Delta$ by the metrics on these spaces. We show that, for r>1 , weak convergence in $\Delta_r$ is slightly more general than convergence in either product topology on $\Delta\times\dots\times\Delta$. We also give several sufficient conditions under which these two modes of convergence are equivalent

A New Metric for Weak Convergence

We introduce a new metric for weak convergence in the space $M^+(S)$ of positive finite measures on the Borel sets of a separable metric space $S$. This metric derives from a norm on the space $M(S)$ of finite rela measures on $S$. Convergence with respect to this norm is not equivalent to weak convergence for measures on $M(S)$ rather than $M^+(S)$

Information Theoretic Interpretation of Forte's Entropy for the Grand Canonical Ensemble

Forte's characterization of the entropy of a grand canonical ensemble in statistical mechanics has a natural interpretation in information theory. This entropy is also shown to be finite under the naturalassumption that the average message length be finite. In the proof, an analogue of the well-known inequality of Shannon is obtained

Two Uniqueness Problems Connected with Lewis' Principle

The application of Lewis's principle depends on the existence and the uniqueness of the solutions of a certain class of variational problems. We show that in two cases of particular physical interest uniquenes can beestablished in a rigorous manner