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GOOD AND BAD MEASURES

Published online by Cambridge University Press:  01 February 2000

P. GURKA ,
F. J. MARTÍN-REYES ,
P. ORTEGA ,
L. PICK ,
M. D. SARRIÓN  and
A. DE LA TORRE
P. GURKA
Affiliation:
Department of Mathematics, Czech University of Agriculture, 165 21 Praha 6, Czech Republic; gurka@tf.czu.cz
F. J. MARTÍN-REYES
Affiliation:
Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 290 71 Málaga, Spain; martin@anamat.cie.uma.es, ortega@anamat.cie.uma.es, torre@anamat.cie.uma.es
P. ORTEGA
Affiliation:
Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 290 71 Málaga, Spain; martin@anamat.cie.uma.es, ortega@anamat.cie.uma.es, torre@anamat.cie.uma.es
L. PICK
Affiliation:
Mathematical Institute, Czech Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic Current address: Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovska ’83, 186 75 Praha 8, Czech Republic; pick@karlin.mff.cuni.cz
M. D. SARRIÓN
Affiliation:
Economía Aplicada (Estadística y Econometría), Facultad de Ciencias Economicas y Empresariales, Universidad de Málaga, 290 71 Málaga, Spain; dsarrion@uma.es
A. DE LA TORRE
Affiliation:
Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 290 71 Málaga, Spain; martin@anamat.cie.uma.es, ortega@anamat.cie.uma.es, torre@anamat.cie.uma.es
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Abstract

The commonly known properties of continuous measures such as the symmetry of the A∞ condition, its equivalence to the reverse Hölder inequality, the left-openness of the Ap condition, etc., are no longer necessarily true when the underlying measure is allowed to have atoms. The measures that preserve these properties are called good measures. The class of good measures is investigated and various criteria for a measure to belong to this class are presented.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 61 , Issue 1 , February 2000 , pp. 123 - 138
Copyright
The London Mathematical Society 2000

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Footnotes

This research was supported by Grant Agency of the Czech Republic grants 201/94/1066 and 201/97/0744, and by University of Wales College of Cardiff, and grant DGES PB97-1097 and the Junta de Andalucía, the Centre de Recerca Matematica, Barcelona.