THEORY OF SCALE-SIMILAR INTERMITTENT MEASURES

It is shown that the concept of scale-similar intermittent measures in troduced by Novikov can be, not only the same as that of the stochasti c multifractal measures argued by Mandelbrot in the context of negativ e fractal dimensions, but also the same as that of the vast class of g eneral stochastic multifractal measures recently introduced by Hentsch el-but only if a substantial condition is added to the process of ense mble averaging. The intrinsic probability characterizing the distribut ion of such a measure is formulated in a general manner so as to be un iquely related to the so-called singularity spectrum f(alpha), the int ermittency exponents mu(q) and the generalized dimensions D(q). The tr ansformation rule of multifractals. the spatial correlations with any power of such a measure and the special utility of generalized Cantor sets as multifractals are demonstrated. Finally, the multifractal natu re of dissipation measure in isotropic turbulence in the inertial rang e, in which scale-similarity is expected, is discussed in terms of the se generalized Canter sets.