Banach-valued probability measures

Interval-Valued Probability Measures

The purpose of this paper is propose a simple de…nition of an interval-valued probability measure and to examine some of the implications of this de…nition. This de…nition provides a method for characterizing certain types of imprecise probabilities. We develop some properties of this de…nition and propose a de…nition of integration with respect to it. We show that this de…nition is a generaliz...

Hyperreal-Valued Probability Measures Approximating a Real-Valued Measure

Constructing Operator Valued Probability Measures in Phase Space

Probability measures (quasi probability mass), given in the form of integrals of Wigner function over areas of the underlying phase space, give rise to operator valued probability measures (OVM). General construction methods of OVMs, are investigated in terms of geometric positive trace increasing maps (PTI), for general 1D domains, as well as 2D shapes e.g. circles, disks. Spectral properties ...

Complex Valued Probability Logics

We present two complex valued probabilistic logics, LCOMPB and LCOMPS , which extend classical propositional logic. In LCOMPB one can express formulas of the form Bz,ρα meaning that the probability of α is in the complex ball with the center z and the radius ρ, while in LCOMPS one can make statements of the form Sz,ρα with the intended meaning – the probability of propositional formula α is in ...

Banach Algebra of Bounded Complex-Valued Functionals

The notation and terminology used in this paper are introduced in the following articles: [2], [16], [9], [14], [7], [8], [3], [18], [17], [4], [19], [5], [15], [1], [20], [12], [11], [10], [21], [13], and [6]. Let V be a complex algebra. A complex algebra is called a complex subalgebra of V if it satisfies the conditions (Def. 1). (Def. 1)(i) The carrier of it ⊆ the carrier of V , (ii) the add...