On the mutual singularity of Hewitt–Stromberg measures for which the multifractal functions do not necessarily coincide

Some Fractal Properties of Sets Having the Moran Structure

“…Possible applications in the spectral theory of self-adjoint operators serve as an additional stimulus for a further investigation of singularly continuous measures [6]. For example, one can note the following researches of singular measures: singularity of Hewitt-Stromberg measures on Bedford-McMullen carpets [2], the mutual singularity of certain measures (see [6,8,24,46,47] and references therein), dimensions of measures [13,20,23].…”

Fractals via Controlled Fisher Iterated Function System

“…Hutchinson's IFS theory has massively expanded for more generalized spaces and generalized contractions, and extended to infinite IFS and multifunction systems to generate general types of fractal sets with the distinguished dimensional measures [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. Hata [32] used condition functions to create IFS.…”