A set C is small if there exists a nonzero measure 
and
an integer n such that
What one typically finds for well-behaved Markov chains on locally compact topological spaces is that every bounded measurable set is small. Chapter 6 of Meyn and Tweedie (1993) gives a number of tools for establishing this property. Here we do it directly for our point process samplers.
Meyn and Tweedie also introduce a concept they call a petite set. For aperiodic Markov chains there is no difference between small and petite sets. Any MHG sampler that has nonzero rejection probabilities, is aperiodic, including Algorithm A. Hence we shall use only the notion of small sets.
