Uniqueness theorems for finitely additive probabilities on quantum structures
-
Marina Svistula
Abstract
The proofs of uniqueness theorems, presented here, allow to extend the earlier results. For example, the following hold: let μ and ν be two finitely additive probabilities on a structure L̃ (for example, L̃ is a pseudo-effect algebra), and let μ be convex-ranged; if there exists an element a ∈ L̃ with 0 < μ(a) < 1 and such that μ(a) = μ(b) ⇒ ν(a) = ν(b) whenever b ∈ L̃, then ν = μ.
References
[1] Avallone, A.—Basile, B.: On a Marinacci uniqueness theorem for measures, J. Math. Anal. Appl. 286 (2003), 378-390.10.1016/S0022-247X(03)00274-9Search in Google Scholar
[2] Avallone, A.—Vitolo, P.: Pseudo-D-lattices and topologies generated by measures, Ital. J. Pure Appl. Math. 29 (2012), 25-42.Search in Google Scholar
[3] Aumann, R.—Shapley, L.: Values of Non-atomic Games, Princeton Univ. Press, Princeton, 1974.10.1515/9781400867080Search in Google Scholar
[4] Bhaskara Rao, M.—Bhaskara Rao, K. P. S.: Charges on Boolean algebras and almost discrete spaces, Mathematika 20, (1973), 214-223.10.1112/S0025579300004800Search in Google Scholar
[5] Dvurečenskij, A.: New quantum structures. In: Handbook of Quantum Logic and Quantum Structures, (K. Engesser, D. M. Gabbay, D. Lehmann, eds.), Elsevier, 2007, pp. 1-53.10.1016/B978-044452870-4/50023-6Search in Google Scholar
[6] Dvurečenskij, A.—Pulmannová, S.: New Trends in Quantum Structures, Kluwer Acad. Publ./Ister Sci., Dordrecht/Bratislava, 2000.10.1007/978-94-017-2422-7Search in Google Scholar
[7] Kannappan, PL.: Functional Equations and Inequalities with Applications, Springer, 2009.10.1007/978-0-387-89492-8Search in Google Scholar
[8] Marinacci, M.: A uniqueness theorem for convex-ranged probabilities, Decis. Econ. Finance 23 (2000), 121-132.10.1007/s102030070003Search in Google Scholar
© 2017 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Some results in local Hilbert algebras
- A note on residuated po-groupoids and lattices with antitone involutions
- The first law of cubology for the Rubik’s Revenge
- Conditional associativity in orthomodular lattices
- A monotonicity property for generalized Fibonacci sequences
- Systems of conditionally independent sets
- On the k-th order lfsr sequence with public key cryptosystems
- On parametric spaces of bicentric quadrilaterals
- Character sums with an explicit evaluation
- Some remarks on formal power series and formal Laurent series
- The co-rank of the fundamental group: The direct product, the first Betti number, and the topology of foliations
- On prime and semiprime generalized hyperaction of hypermonoid
- On O’Malley ϱ-upper continuous functions
- Uniqueness theorems for finitely additive probabilities on quantum structures
- Some results on differential-difference analogues of Brück conjecture
- Oscillation of neutral second order half-linear differential equations without commutativity in deviating arguments
- On support, separation and decomposition theorems for t-Wright-concave functions
- A characterization of holomorphic bivariate functions of bounded index
- Asymptotic expansion of double Laplace-type integrals with a curve of minimal points and application to an exit time problem
- The geometry of two-valued subsets of Lp-spaces
- Hemi-slant submanifolds as warped products in a nearly Kaehler manifold
- A comparison of two tests in multivariate models
- Modelling prescription behaviour of general practitioners
- Characterization of congruence lattices of principal p-algebras
Articles in the same Issue
- Some results in local Hilbert algebras
- A note on residuated po-groupoids and lattices with antitone involutions
- The first law of cubology for the Rubik’s Revenge
- Conditional associativity in orthomodular lattices
- A monotonicity property for generalized Fibonacci sequences
- Systems of conditionally independent sets
- On the k-th order lfsr sequence with public key cryptosystems
- On parametric spaces of bicentric quadrilaterals
- Character sums with an explicit evaluation
- Some remarks on formal power series and formal Laurent series
- The co-rank of the fundamental group: The direct product, the first Betti number, and the topology of foliations
- On prime and semiprime generalized hyperaction of hypermonoid
- On O’Malley ϱ-upper continuous functions
- Uniqueness theorems for finitely additive probabilities on quantum structures
- Some results on differential-difference analogues of Brück conjecture
- Oscillation of neutral second order half-linear differential equations without commutativity in deviating arguments
- On support, separation and decomposition theorems for t-Wright-concave functions
- A characterization of holomorphic bivariate functions of bounded index
- Asymptotic expansion of double Laplace-type integrals with a curve of minimal points and application to an exit time problem
- The geometry of two-valued subsets of Lp-spaces
- Hemi-slant submanifolds as warped products in a nearly Kaehler manifold
- A comparison of two tests in multivariate models
- Modelling prescription behaviour of general practitioners
- Characterization of congruence lattices of principal p-algebras
