  For infinite binary sequences, the Martin-Löf definition in terms of effective tests is a robust and mathematically attractive notion. However, it seems to have the major flaw that it applies only to infinite binary sequences. (Since finiteness of a sequence is effectively positively decidable, and the set of all finite sequences is measure zero, every finite sequence violates an effective measure one randomness property.) Yet ordinarily we are happy to characterise even quite small finite sequences of outcomes as random. As mentioned  above  (§2),  there is room for doubt at our ability to do so correctly, as we seem to be prone to mischaracterise sequences we are presented with, and perform poorly when asked to produce our own random sequences. However, there is nothing in this literature to suggest that we are fundamentally mistaken in applying the notion of randomness to finite sequences at all. So one might think this shows that the Martin-Löf approach is too restrictive.