Positivity (2012) 16:393
Erratum to: Markov processes on Riesz spaces
Jessica J. Vardy · Bruce A. Watson
Published online: 13 July 2011
© Springer Basel AG 2011
Erratum to: Positivity
In Definition 3 of this article, a condition has been omitted.
Definition 3 should read (i.e. the italicized words below were omitted):
Deﬁnition 3 Let E be a Dedekind complete Riesz space with conditional expectation
T and weak order unit e = Te.LetP and Q be band projections on E, we say that P
and Q are T -conditionally independent with respect to T if
TPTQe = TPQe = TQTPe. (1)
We say that twoRiesz subspaces E
of E, containing R(T ),areT -conditionally
independent with respect to T if all band projections P
, i = 1, 2, in E with
e ∈ E
, i = 1, 2, are T -conditionally independent with respect to T .
Acknowledgments We thank Prof. J.J. Grobler for alerting us to the omission corrected herein.
The online version of the original article can be found under doi:10.1007/s11117-011-0121-0.
J. J. Vardy · B. A. Watson (
Centre for Applicable Analysis and Number Theory, School of Mathematics,
University of the Witwatersrand, Private Bag 3, P.O.WITS, Johannesburg 2050, South Africa