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Ergodicity of Markov processes via non-standard analysisProbability
2016 A time-homogeneous Markov process with a stationary probability distribution π will converge to π in an appropriate sense (i.e., will be “ergodic”), under suitable conditions (such as “irreducibility”). This phenomenon is well understood for processes in discrete time and space, and for processes in continuous time and discrete space (see e.g. ), and for processes in discrete time and continuous space. However, for processes in continuous time and space, there are apparently no such clean results; the closest are apparently the results in using awkward assumptions about skeleton chains (see Section 5 below)...
Generalized symmetric systems and thin-very tall compact scattered spacesarXiv
Variations on ω-boundednessIsrael Journal of Mathematics
2013 Let be a property (or, equivalently, a class) of topological spaces. A space X is called-bounded if every subspace of X with (or in) has compact closure. Thus, countable-bounded has been known as ω-bounded and (σ-compact)-bounded as strongly ω- ...
2012 A function of two variables F (x, y) is universal iff for every other function G (x, y) there exists functions h (x) and k (y) with G (x, y)= F (h (x), k (y)) Sierpinski showed that assuming the continuum hypothesis there exists a Borel function F (x, y) which is universal ...