Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The Lebesgue decomposition theorem for partially ordered semigroup-valued measures

Author: Panaiotis K. Pavlakos
Journal: Proc. Amer. Math. Soc. 71 (1978), 207-211
MSC: Primary 46G10; Secondary 28A55
MathSciNet review: 0487449
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The present paper is concerned with partially ordered semigroup-valued measures. Below are given generalizations of the classical Lebesgue Decomposition Theorem. These results can be applied to Stone or ${W^ \ast }$ algebra-valued positive measures (cf. [3], [12], [13], [14]).

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46G10, 28A55

Retrieve articles in all journals with MSC: 46G10, 28A55

Additional Information

Keywords: Partially ordered semigroup, monotone complete partially ordered semigroup, partially ordered semigroup of the countable type, <I>o</I>-measure, absolutely continuous and singular <I>o</I>-measure, partially ordered topological semigroup, <IMG WIDTH="18" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="$\sigma$">-compatible topology with the partial ordering, <IMG WIDTH="30" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${\tau _X}$">-measure
Article copyright: © Copyright 1978 American Mathematical Society