# Ordered representations of spaces of integrable functions

Ordered representations of spaces of integrable functions Let X be a Banach space, (Ω,Σ) a measurable space and let m : Σ → X be a (countably additive) vector measure. Consider the corresponding space of integrable functions L 1(m). In this paper we analyze the set of (countably additive) vector measures n satisfying that L 1(n) = L 1(m). In order to do this we define a (quasi) order relation on this set to obtain under adequate requirements the simplest representation of the space L 1(m) associated to downward directed subsets of the set of all the representations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Ordered representations of spaces of integrable functions

, Volume 13 (1) – Sep 1, 2008
15 pages

Loading next page...

/lp/springer_journal/ordered-representations-of-spaces-of-integrable-functions-0NFP7l0jKt
Publisher
Springer Journals
Copyright
Copyright © 2008 by Birkhäuser Verlag Basel/Switzerland
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-008-2211-1
Publisher site
See Article on Publisher Site

### Abstract

Let X be a Banach space, (Ω,Σ) a measurable space and let m : Σ → X be a (countably additive) vector measure. Consider the corresponding space of integrable functions L 1(m). In this paper we analyze the set of (countably additive) vector measures n satisfying that L 1(n) = L 1(m). In order to do this we define a (quasi) order relation on this set to obtain under adequate requirements the simplest representation of the space L 1(m) associated to downward directed subsets of the set of all the representations.

### Journal

PositivitySpringer Journals

Published: Sep 1, 2008

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just \$49/month

### Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

### Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

### Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

### Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

DeepDyve

DeepDyve

### Pro

Price

FREE

\$49/month
\$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off