Abstract
Let S-i : R-d -> R-d for i = 1,...,N be contracting similarities. Also, let (P-1, - - -, P-N, P) be a probability vector and let nu be a probability measure on R-d with compact support. Then there exists a unique probability measure mu on R-d such that
mu = Sigma P-i(i)mu circle S-i(-1) + P nu
The mesure mu is called an in-homogenous self-similar measure.
| Original language | English |
|---|---|
| Pages (from-to) | 1789-1844 |
| Number of pages | 56 |
| Journal | Indiana University Mathematics Journal |
| Volume | 57 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 2008 |
Keywords
- multifractals
- multifractal spectra
- L-q spectra
- in-homogenous self-similar measure
- in-homogenous self-similar set
- self-similar measure
- ITERATED FUNCTION SYSTEMS
- BERNOULLI CONVOLUTIONS
- PHASE-TRANSITIONS
- DELETED DIGITS
- FRACTALS
- FORMALISM
- EXPANSIONS
- DIMENSIONS