Abstract
The purpose of this paper twofold. Firstly, we establish -completeness and -completeness of several different classes of multifractal decomposition sets of arbitrary Borel measures (satisfying a mild non-degeneracy condition and two mild “smoothness” conditions). Secondly, we apply these results to study the -completeness and -completeness of several multifractal decomposition sets of self-similar measures (satisfying a mild separation condition). For example, a corollary of our results shows if is a self-similar measure satisfying the strong separation condition and is not equal to the normalized Hausdorff measure on its support, then the classical multifractal decomposition sets of defined by are -complete provided they are non-empty.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
