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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Measures of concordance determined by $D_4$-invariant measures on $(0,1)^2$


Authors: H. H. Edwards, P. Mikusinski and M. D. Taylor
Journal: Proc. Amer. Math. Soc. 133 (2005), 1505-1513
MSC (2000): Primary 62H05, 62H20
Published electronically: November 19, 2004
MathSciNet review: 2111952
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Abstract: A measure, $\mu$, on $(0,1)^2$ is said to be $D_4$-invariant if its value for any Borel set is invariant with respect to the symmetries of the unit square. A function, $\kappa$, generated in a certain way by a measure, $\mu$, on $(0,1)^2$ is shown to be a measure of concordance if and only if the generating measure is positive, regular, $D_4$-invariant, and satisfies certain inequalities. The construction examined here includes Blomqvist's beta as a special case.


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Additional Information

H. H. Edwards
Affiliation: Department of Mathematics, University of Central Florida, P.O. Box 161364, Orlando, Florida 32816-1364
Email: newcopulae@yahoo.com

P. Mikusinski
Affiliation: Department of Mathematics, University of Central Florida, P.O. Box 161364, Orlando, Florida 32816-1364
Email: piotrm@mail.ucf.edu

M. D. Taylor
Affiliation: Department of Mathematics, University of Central Florida, P.O. Box 161364, Orlando, Florida 32816-1364
Email: mtaylor@pegasus.cc.ucf.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07641-5
PII: S 0002-9939(04)07641-5
Received by editor(s): August 1, 2003
Received by editor(s) in revised form: November 11, 2003, and January 13, 2004
Published electronically: November 19, 2004
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2004 American Mathematical Society