The other prime example of a fine topology is the fine topology of potential theory (in the usual sense of electromagnetism, gravitation, etc.) This is finer than the Euclidean topology but coarser than the density topology. Each of these three topologies has its σ-ideal of small sets: the meagre sets for the Euclidean case, the polar sets for the fine topology of potential theory, and the (Lebesgue-)null sets for the density topology. The polar sets have been extensively studied, not only in potential theory as above but in probabilistic potential theory; pioneers here include P.-A. Meyer and J. L. Doob. Relevant here are the links between martingales and harmonic functions (likewise their sub- and super-versions), Green functions, Green domains, Markov processes, Brownian motion, Dirichlet forms, energy and capacity. The general theory of such fine topologies involves such things as analytically heavy topologies, base operators, density operators and lifting.