Sequences in the range of a vector measure with bounded variation
Sequences in the range of a vector measure with bounded variation
Let <italic>X</italic> be a Banach space. We consider sequences <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis x Subscript n Baseline right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>x</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">({x_n})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in <italic>X</italic> lying in the range of a measure valued in a …