We construct and study space homogeneous and isotropic random measures (MMRM) which generalize the so-called MRM measures constructed by previous authors. Our measures satisfy an exact scale invariance equation and are therefore natural models in dimension 3 for the dissipation measure in a turbulent flow.
"Multidimensional Multifractal Random Measures." Electron. J. Probab. 15 241 - 258, 2010. https://doi.org/10.1214/EJP.v15-746