In the present communication a generalized cost measure of utilities and lengths of output codewords from a memoryless source are defined. Lower and upper bounds in terms of a non-additive generalized measure of ‘useful’ information are obtained.

Finitely-additive measures invariant to the action of some groups on a separable infinitedimensional real Hilbert space are constructed. The invariantness measure is studied with respect group shifts vector space, orthogonal and symplectomorphisms equipped shift-invariant symplectic form. A considered locally finite, σ but it not countably additive. analog ergodic decomposition finitely additiv...

Weighted kappa is a measure that is commonly used for quantifying similarity between two ordinal variables with identical categories. Additive kappa is a special case of weighted kappa that allows the researcher to specify distances between adjacent categories. It is shown that additive kappa is a weighted average of the additive kappas of all collapsed tables of a specific size. It follows tha...

The changes in the unitary polar factor under both multiplicative and additive perturbation are studied. A multiplicative perturbation bound and a new additive perturbation bound, in which a different measure of perturbation is introduced, are presented. AMS subject classification (2000): 15A18, 15A23, 65F35.

Stochastic nonlinear elliptic partial differential equations with white noise disturbances are studied in the countably additive measure set up. Introducing the Onsager-Machlup function to the system model, the smoothing problem for maximizing the modified likelihood functional is solved and the explicit form of nonlinear smoother is presented in the finitely additive observation noise set up. ...

We propose a situation calculus formalization of action domains that include numeric-valued fluents (so-called additive or measure fluents) and concurrency. Our approach allows formalizing concurrent actions whose effects increment/decrement the value of additive fluents. For describing indirect effects, we employ mathematical equations in a manner that is inspired by recent work on causality a...

We present a necessary and sufficient condition for a Boolean algebra to carry a finitely additive measure.

Fuzzy random variables have been introduced by Puri and Ralescu as an extension of random sets. In this paper, we ®rst introduce a real-valued generalized measure of the ``relative variation'' (or inequality) associated with a fuzzy random variable. This measure is inspired in Csisz ar's f-divergence, and extends to fuzzy random variables many well-known inequality indices. To guarantee certain...