Abstract
For a probability measure mu on a subset of R-d, the lower and upper L-q-dimensions of order q epsilon R are defined by
(D) under bar (mu)(q) = lim(r SE arrow 0)inf log integral mu(B(x, r))(q-1)d mu(x)/-logr,
(D) over bar (mu)(q) = lim(r SE arrow 0)sup log integral mu(B(x, r))(q-1)d mu(x)/-logr.
In previous work we studied the typical behaviour (in the sense of Baire's category) of the L-q-dimensions (D) under bar (mu)(q) and (D) over bar (mu)(q) for q >= 1. In the present work we study the typical behaviour (in the sense of Baire's category) of the upper L-q-dimensions SAS. (C) 2007 Elsevier Masson SAS. All rights reserved.
Original language | English |
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Pages (from-to) | 551-561 |
Number of pages | 11 |
Journal | Bulletin des Sciences Mathématiques |
Volume | 132 |
DOIs | |
Publication status | Published - Oct 2008 |
Keywords
- Multifractals
- L-q-dimensions
- Baire category
- Residual set
- FRISCH-PARISI CONJECTURE