Fractal percolation, porosity, and dimension

Abstract We study the porosity properties of fractal percolation sets E ⊂ Rd. Among other things, for all 0 < ɛ < ½, we obtain dimension bounds for the set of exceptional points where the upper porosity of E is less than ½ ‒ ɛ, or the lower porosity is larger than ɛ. Our method works also for inhomogeneous fractal percolation and more general random sets whose offspring distribution gives rise to a Galton–Watson process