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Contributors
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- By Shamsuddin Akhtar, Greg Albert, Sidney Allison, Muhammad Anwar, Haruo Arita, Amanda Barker, Mary Hanna Bekhit, Jeanna Blitz, Tyson Bolinske, David Burbulys, Asokumar Buvanendran, Gregory Cain, Keith A. Candiotti, Daniel B. Carr, Derek Chalmers, John Charney, Rex Cheng, Roger Chou, Keun Sam Chung, Anna Clebone, Frederick Conlin, Susan Dabu-Bondoc, Tiffany Denepitiya-Balicki, Jeanette Derdemezi, Anahat Kaur Dhillon, Ho Dzung, Juan Jose Egas, Stephen M. Eskaros, Zhuang T. Fang, Claudia R. Fernandez Robles, Victor A. Filadora, Ellen Flanagan, Dan Froicu, Allison Gandey, Nehal Gatha, Boris Gelman, Christopher Gharibo, Muhammad K. Ghori, Brian Ginsberg, Michael E. Goldberg, Jeff Gudin, Thomas Halaszynski, Martin Hale, Dorothea Hall, Craig T. Hartrick, Justin Hata, Lars E. Helgeson, Joe C. Hong, Richard W. Hong, Balazs Horvath, Eric S. Hsu, Gabriel Jacobs, Jonathan S. Jahr, Rongjie Jaing, Inderjeet Singh Julka, Zeev N. Kain, Clinton Kakazu, Kianusch Kiai, Mary Keyes, Michael M. Kim, Peter G. Lacouture, Ryan Lanier, Vivian K. Lee, Mark J. Lema, Oscar A. de Leon-Casasola, Imanuel Lerman, Philip Levin, Steven Levin, JinLei Li, Eric C. Lin, Sharon Lin, David A. Lindley, Ana M. Lobo, Marisa Lomanto, Mirjana Lovrincevic, Brenda C. McClain, Tariq Malik, Jure Marijic, Joseph Marino, Laura Mechtler, Alan Miller, Carly Miller, Amit Mirchandani, Sukanya Mitra, Fleurise Montecillo, James M. Moore, Debra E. Morrison, Philip F. Morway, Carsten Nadjat-Haiem, Hamid Nourmand, Dana Oprea, Sunil J. Panchal, Edward J. Park, Kathleen Ji Park, Kellie Park, Parisa Partownavid, Akta Patel, Bijal Patel, Komal D. Patel, Neesa Patel, Swati Patel, Paul M. Peloso, Danielle Perret, Anthony DePlato, Marjorie Podraza Stiegler, Despina Psillides, Mamatha Punjala, Johan Raeder, Siamak Rahman, Aziz M. Razzuk, Maggy G. Riad, Kristin L. Richards, R. Todd Rinnier, Ian W. Rodger, Joseph Rosa, Abraham Rosenbaum, Alireza Sadoughi, Veena Salgar, Leslie Schechter, Michael Seneca, Yasser F. Shaheen, James H. Shull, Elizabeth Sinatra, Raymond S. Sinatra, Neil Singla, Neil Sinha, Denis V. Snegovskikh, Dmitri Souzdalnitski, Julie Sramcik, Zoreh Steffens, Alexander Timchenko, Vadim Tokhner, Marc C. Torjman, Co T. Truong, Nalini Vadivelu, Ashley Vaughn, Anjali Vira, Eugene R. Viscusi, Dajie Wang, Shu-ming Wang, J. Michael Watkins-Pitchford, Steven J. Weisman, Ira Whitten, Bryan S. Williams, Jeremy M. Wong, Thomas Wong, Christopher Wray, Yaw Wu, Anthony T. Yarussi, Laurie Yonemoto, Bita H. Zadeh, Jill Zafar, Martha Zegarra, Keren Ziv
- Edited by Raymond S. Sinatra, Jonathan S. Jahr, University of California, Los Angeles, School of Medicine, J. Michael Watkins-Pitchford
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- Book:
- The Essence of Analgesia and Analgesics
- Published online:
- 06 December 2010
- Print publication:
- 14 October 2010, pp xi-xviii
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- Chapter
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ON THE CENTRED HAUSDORFF MEASURE
- ALEXANDER SCHECHTER
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- Journal:
- Journal of the London Mathematical Society / Volume 62 / Issue 3 / December 2000
- Published online by Cambridge University Press:
- 19 February 2001, pp. 843-851
- Print publication:
- December 2000
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- Article
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Let v be a measure on a separable metric space. For t, q ∈ R, the centred Hausdorff measures μh with the gauge function h(x, r) = rt(vB(x, r))q is studied. The dimension defined by these measures plays an important role in the study of multifractals. It is shown that if v is a doubling measure, then μh is equivalent to the usual spherical measure, and thus they define the same dimension. Moreover, it is shown that this is true even without the doubling condition, if q [ges ] 1 and t [ges ] 0 or if q [les ] 0. An example in R2 is also given to show the surprising fact that the above assertion is not necessarily true if 0 < q < 1. Another interesting question, which has been asked several times about the centred Hausdorff measure, is whether it is Borel regular. A positive answer is given, using the above equivalence for all gauge functions mentioned above.