In this paper, we give a new vectorial multifractal formalism for which the classical multifractal formalism does not hold. We precisely introduce and study a vectorial multifractal formalism based on the Hewitt-Stromberg measures This formalism is parallel to Peyrière's vertorial multifractal formalism which is based on the Hausdorff and packing measures. Mathematics Subject Classification: 28A78, 28A80 

A relative vectorial multifractal formalism

A Relative Vectorial Multifractal Formalism

Addendum to: A Note on Fractal Measures and Cartesian Product Sets

In this note, we investigate those Hewitt Stromberg measures which obey to a
 simple scaling law. Consider a dimension function h and let Hh be the
 corresponding Hewitt Stromberg measure. We say that Hh obeys an order ?
 scaling law whenever taking A ? Rm and c > 0, one has Hh(cA) = c?Hh(A).

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A note on scaling properties of Hewitt Stromberg measure

A note on the Regularities of Hewitt-Stromberg h-measures

In this paper, we give a new product formula : $$\begin{aligned} {\mathsf {H}}^t(E) {\mathsf {H}}^s(F)\le c_1 {\mathsf {H}}^{t+s}(E\times F)\le & {} c_2 {\mathsf {H}}^s(E) {\mathsf {P}}^t(F)\\\le & {} c_3 {\mathsf {P}}^{t+s}(E\times F) \le c_4 {\mathsf {P}}^s(E) {\mathsf {P}}^t(F). \end{aligned}$$
 where $$E\subseteq \mathbb {R}^d$$
 , $$F\subseteq \mathbb {R}^l$$
 , $$t,s\ge 0$$
 and $$ {\mathsf {H}}^t$$
 and $${\mathsf {P}}^s$$
 denote, respectively, the lower and upper Hewitt–Stromberg measures. Using these inequalities, we give lower and upper bounds for the lower and upper Hewitt–Stromberg dimensions $${\mathsf {b}}(E\times F)$$
 and $${\mathsf {B}}(E\times F)$$
 in terms of the Hewitt–Strombeg dimensions of E and F.

Meriem Ben Hadj Khlifa

Papers

A Note on Fractal Measures and Cartesian Product Sets

The single anastomosis sleeve ileal (SASI) bypass: A review of the current literature on outcomes and statistical results