We present an abstract approach on probability measures, events and random
variables, involving in particular lattice theory, distance functions, σ-additive
extensions of finitely additive functions, some kinds of convergences in the lattice
setting, which can be considered even in more abstract contexts. Furthermore we pose
some open problems.
Keywords: Almost uniform convergence, attribute, Boolean algebra, Boolean σ-
algebra, concept, distance function, duality principle, experiment, finitely additive
function, lattice, normalized distance, object, order convergence, probability,
random variable, regular lattice, subsemilattice, supersemilattice, σ-additive
function, σ-regular lattice.