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ON THE CONTINUITY OF THE SEMIVARIATION IN LOCALLY CONVEX SPACES

ON THE CONTINUITY OF THE SEMIVARIATION IN LOCALLY CONVEX SPACES,J An Haluska

ON THE CONTINUITY OF THE SEMIVARIATION IN LOCALLY CONVEX SPACES   (Citations: 5)
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Abstract. If the introduced condition (GB) is fulfllled, then everywhere conver- gence of nets of measurable functions implies convergence in semivariation on a set of flnite variation of a measure,m: § ! L(X;Y) which is æ-additive in the strong operator topology (§ is a æ-algebra of subsets and X;Y are both locally convex spaces). In the case of the purely atomic measure Condition (GB) is fulfllled.
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