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2005-2006 Topologizing the Denjoy space by measuring equiintegrability.
J. Alan Alewine, Eric Schechter
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Real Anal. Exchange 31(1): 23-44 (2005-2006).


Basic limit theorems for the KH integral involve equiintegrable sets. We construct a family of Banach spaces $X_\Delta$ whose bounded sets are precisely the subsets of ${\cal KH}[0,1]$ that are equiintegrable and pointwise bounded. The resulting inductive limit topology on $\bigcup_\Delta X_\Delta = {\cal KH}[0,1]$ is barreled, bornological, and stronger than both pointwise convergence and the topology given by the Alexiewicz seminorm, but it lacks the countability and compatibility conditions that are often associated with inductive limits.


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J. Alan Alewine. Eric Schechter. "Topologizing the Denjoy space by measuring equiintegrability.." Real Anal. Exchange 31 (1) 23 - 44, 2005-2006.


Published: 2005-2006
First available in Project Euclid: 5 June 2006

zbMATH: 1129.26003
MathSciNet: MR2218186

Primary: 26A39

Keywords: barreled , convergence rate , Denjoy space , equiintegrable , Henstock integral , inductive limit , KH integral , Kurzweil integral , norm

Rights: Copyright © 2005 Michigan State University Press

Vol.31 • No. 1 • 2005-2006
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