On Feller continuity and full abstraction

We study the nature of applicative bisimilarity in λ-calculi endowed with operators for sampling from contin- uous distributions. On one hand, we show that bisimilarity, logical equivalence, and testing equivalence all coincide contextual when real numbers can be manipulated through continuous functions only. The key ingredient towards this result is a notion Feller-continuity labelled Markov processes, which believe independent interest, giving rise broad class LMPs coinductive logically inspired equivalences coincide. other if no constraint put on way are manipulated, characterizing turns out to hard, most aforementioned notions even unsound.