Handbook of Heavy Tailed Distributions in Finance

10 A noteworthy and unexpected separation of roles, between the “dimensionspectrum” and the total mass Ω; the former is ruled by the accessible α forwhich f(α) > 0, the latter, by the inaccessible α for which f(α) < 0

Brought together, Sections 4, 7, 8, and 9 imply, in plain words, that what you do not necessarily see may affect you significantly. This section serves to underline that the notion of canonical multifractal is very subtle and deserves to be well-understood and further discussed.

10.1 Definitions of the “accessible ranges” of the variables: qs from $q_{\min }^{*}$ to $q_{\max }^{*}$and αs from ${\alpha }_{\max }^{*}$ to ${\alpha }_{\max }^{*}$; the accessible functions τ* (q)and f* (α)

Mandelbrot ...