On extensions of Rényi conditional probability spaces

Conditional Probability Spaces

Improper priors are used frequently, but often formally and without reference to a sound theoretical basis. The present paper demonstrates that Kolmogorov’s (1933) formulation of probability theory admits a minimal generalization which includes improper priors and a general Bayes theorem. The resulting theory is closely related to the theory of conditional probability spaces formulated by Renyi...

A Preferred Definition of Conditional Rényi Entropy

The Rényi entropy is a generalization of Shannon entropy to a one-parameter family of entropies. Tsallis entropy too is a generalization of Shannon entropy. The measure for Tsallis entropy is non-logarithmic. After the introduction of Shannon entropy , the conditional Shannon entropy was derived and its properties became known. Also, for Tsallis entropy, the conditional entropy was introduced a...

On the Conditional Rényi Entropy

Regular Conditional Probability, Disintegration of Probability and Radon Spaces

We establish equivalence of several regular conditional probability properties and Radon space. In addition, we introduce the universally measurable disintegration concept and prove an existence result.

Stable Beliefs and Conditional Probability Spaces

This thesis aims to provide a conceptual framework that unifies Leitgeb’s theory of stable beliefs, Battigalli-Siniscalchi’s notion of strong belief and the notions of core, a priori, abnormal and conditional belief studied by Van Fraassen and Arló-Costa. We will first present the difficulties of modeling qualitative notions of belief and belief revision in a quantitative probabilistic setting....