Vol. 95, No. 1, 1981

Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
Vector-valued functions as families of scalar-valued functions

Robert F. Geitz and J. Jerry Uhl, Jr.

Vol. 95 (1981), No. 1, 75–83
Abstract

One time-honored way of studying the properties of a vector measure F with values in a Banach space X, with dual X is to examine properties of the family of scalar measures {⟨x,F: xX,x1}. The purpose of this paper is to undertake a similar study for vector-valued functions. The first theorem proved in this vein was the classical Pettis measurability theorem which states that if X is a separable Banach space and f is an X-valued function such that x,fis measurable for each x in X, then f is a measurable function. What we propose to do is to take a bounded function f with values in X, form the associated family = {⟨x,f: xX,x1} and study how measurability and integrability properties of f are reflected by topological properties of in the spaces L and B(Σ).

Mathematical Subject Classification 2000
Primary: 28B99
Secondary: 46G10
Milestones
Received: 25 September 1979
Revised: 30 July 1980
Published: 1 July 1981
Authors
Robert F. Geitz
J. Jerry Uhl, Jr.