Abstract
Let V denote a ring of subsets of an abstract space X, let R denote the real numbers, and let N denote the positive integers. Denote by a(V, R) (respectively ca(V, R)) the space of real valued, finitely additive (respectively countably additive) functions on the ring V and denote by ab(V, R) the subspace consisting of those members of the space a(V, R) with finite variation on each set in the ring V. Members of the space a(V, R) are referred to as charges and members of the space ab(V, R) are referred to as locally bounded charges. We denote by cab(V, R) the intersection of the spaces ab(V, R) and ca(V, R).
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