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In [3], [6], some Vitali-Hahn-Saks and Nikodym-type theorems are proved about the measures on a Boolean algebra 9? with the interpolation property, called the property I. In this note we prove that these results are simple consequences of well-known results. For a Hausdorff locally convex space E, always assumed to be over K, the field of real or complex numbers, E' will denote its topological dual [4]. A Hausdorff Abelian topological group G is called normed if there exists a function *: G -> [0, oo) satisfying the conditions (i) IxI = 0 x = 0, (ii) Ix + yl S x I + IyI, such that the topology of G comes from the metric P, P(x, y) = Ix yj [1]. A Boolean algebra 9f is said to have the property I if for any two sequences {x,,}, (Ym}1 in 9? with X,, T, Ym J, and x, < ym, Vm, n, there exists an x E 9f such that xn < x < ym, Vm, n [5]. We shall use the theory of submeasures developed in [1] (in [1], submeasures are defined on the algebra of subsets of a set; by considering the clopen subsets of the Boolean space of a Boolean algebra, they can be defined on a Boolean algebra).

Some remarks on the sequences of exhaustive measures and uniform boundedness of measures