𝐿₀-valued vector measures are bounded

Abstract

Every vector measure taking values in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L 0 left-parenthesis 0 comma 1 right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>L</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">{L_0}(0,1)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> has bounded range.

Locations

• Proceedings of the American Mathematical Society - View - PDF