标题：Bounded sets in the range
of an <mml:math alttext="$X^**$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>X</mml:mi><mml:mrow><mml:mo>∗</mml:mo><mml:mo>∗</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>-valued measure with
bounded variation
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2000
卷号：23
DOI：10.1155/S0161171200001708
出版社：Hindawi Publishing Corporation
摘要：Let X be a Banach space and A⊂X an absolutely
convex, closed, and bounded set. We give some sufficient and necessary
conditions in order that A lies in the range of a measure valued in the bidual space X∗∗ and having bounded
variation. Among other results, we prove that X∗ is a G. T.-space if and only if A lies inside the range of some
X∗∗-valued measure with bounded variation whenever XA is isomorphic to a Hilbert space.
