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Abstract It is shown that in general non-linear quasi-states will exist on C ( X ), where X is a compact Hausdorff space. We introduce the concept of a quasi-measure in X and establish the connection… (More)
The main result of the paper provides a method for construction of regular non-subadditive measures in compact Hausdorff spaces. This result is followed by several examples. In the last section it is… (More)
Let X be a compact Hausdorff space, and let c (respectively o) denote the collection of closed (respectively open) subsets of X . Let a c [ o. A quasi-measure in X is a function :a! R which is… (More)
Am apρ : C(X) → C(Y) is called quasi-linear if it is linear on each singly generated subalgebra of C(X). We prove the representation theorem for positive quasi-linear functionals in terms of… (More)
We introduce a class of set-functions on the set of natural numbers, which are called super-measures. Super-measures are then utilized to characterize a certain class of topological measures… (More)
SummaryThis paper introduces a novel idea: the concept of an image transformation. We also introduce the closely related concept of a quasi-homomorphism, and study the properties of these… (More)