Skip to main content Accessibility help
×
Home
Hostname: page-component-55597f9d44-t4qhp Total loading time: 0.431 Render date: 2022-08-18T20:41:35.275Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

GOOD AND BAD MEASURES

Published online by Cambridge University Press:  01 February 2000

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
Get access

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
Copyright
The London Mathematical Society 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.
4
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

GOOD AND BAD MEASURES
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

GOOD AND BAD MEASURES
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

GOOD AND BAD MEASURES
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *