The information deviation between any two finite measures cannot be increased by any statistical operations (Markov morphisms). It is invarient if and only if the morphism is sufficient for these two measures

Explicit formulas for the metric and affine connections on the space of finite measures and probability measures are derived in different coordinate systems. They are transformed and compared with previous formulas of Cencov, Amari, and others. These formulas are given for finite sample spaces...

Existing experiments do not disprove local realistic quantum theories. To overcome logical difficulties of the standard quantum theory, a nondeterministic irreversible local realistic theory was proposed, in which the wave-particle duality is objective in contrast to the complementarity...

In statistics it is necessary to study the relation among many probability distributions. Information geometry elucidates the geometric structure on the space of all distributions. When combined with Bayesian decision theory, it leads to the new concept of "ideal estimates." They uniquely exist...

Statistics requires consideration of the ``ideal estimates'' defined through the posterior mean of fractional powers of finite measures. In this paper we study , the linear space spanned by th power of finite measures, . It is shown that generalizes the Lebesgue function space , and shares most...

The standard quantum theory is mathematically incompatible with irreversible macroscopic theories. An alternative irreversible quantum theory is proposed, which also provides an explanation of measurement as a physical process. It is based on the postulate that the physical world is governed by...