This chapter contains some known results on connectivity which are used later on. The notion of unicoherence of a simply-connected set is explained and extended to lattices. Peierls (counting) arguments are described for estimating the number of connected sets in the lattice, and elements of (lattice) percolation theory are described. A multiparameter ergodic theorem is given, and the basic theory of continuum percolation is described. Some of the theory of Poisson point processes are recalled, including the superposition, thinning, and scaling theorems.
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