The assertion in question comes from the short final section in the Theory of Capacities of Choquet 1953/54, in connection with his prototype of the subsequent Choquet integral. The problem was whether and when this formation is additive. Choquet had the much more abstract idea that all functionals in a certain wide class must be subadditive, and the counterpart with superadditive. His treatmen...

This paper provides a Lyapunov-based small-gain theorem for input-to-state stability (ISS) of networks composed infinitely many finite-dimensional systems. We model these on infinite-dimensional ? ? -type spaces. A crucial assumption in our results is that the internal Lyapunov gains, modeling influence subsystems each other, are linear functions. Moreover, gain operator built from gains assume...

This paper provides necessary and sufficient conditions for the existence of a pure strategy Bertrand equilibrium in a model of price competition with fixed costs. It unveils an interesting and unexplored relationship between Bertrand competition and natural monopoly. That relationship points out that the non-subadditivity of the cost function at the output level corresponding to the oligopoly ...

For a non-autonomous dynamics with discrete time defined by tempered sequence of upper-triangular matrices, we obtain lower and upper bounds for the Grobman regularity coefficients. We also give two applications these results: an bound coefficients exterior powers sequence, simple proof Oseledets' multiplicative ergodic theorem cocycles over measure-preserving transformation without using Kingm...

Let L be a lattice ordered effect algebra. We prove that the lattice uniformities on L which make uniformly continuous the operations ⊖ and ⊕ of L are uniquely determined by their system of neighbourhoods of 0 and form a distributive lattice. Moreover we prove that every such uniformity is generated by a family of weakly subadditive [0,+∞]-valued functions on L.

We prove a theorem about subdirect decompositions of lattice effect algebras. Further, we show how, under these decompositions, blocks, sets of sharp elements and centers of those effect algebras are decomposed. As an application we prove a statement about the existence of subadditive state on some block-finite effect algebras.

Let (L, ∗) be a semilattice, and let c : L → [0,∞) be monotone and increasing on L. We state the Minimum Join problem as: given size n sub-collection X of L and integer k with 1 ≤ k ≤ n, find a size k sub-collection (x1, x ′ 2, . . . , x ′ k) of X that minimizes c(x ′ 1 ∗ x2 ∗ · · · ∗ xk). If c(a ∗ b) ≤ c(a) + c(b) holds, we call this the Minimum Subadditive Join (MSJ) problem and present a gre...