Coherent updating on finite spaces
We compare the dierent notions of conditional coherence within the behavioural theory of imprecise probabilities when all the spaces are finite. We show that the dierences between the notions are due to conditioning on sets of (lower, and in some cases upper) probability zero. Next, we characterise the range of coherent extensions, proving that the greatest coherent extensions can always be calculated using the notion of regular extension.