[cf. fairly; see also: somewhat, quite, instead
Rather than discuss this in full generality, let us look at a particular situation of this kind.
Rather than using the definition of...... we shall use the fact that......
However, F is only nonnegative rather than strictly positive, as one may have expected.
The definition is stated in terms of local martingales, rather than martingales, for the technical reason that the former are easier to characterize in applications.
It seems that the relations between these concepts emerge most clearly when the setting is quite abstract, and this (rather than a desire for mere generality) motivates our approach to the subject.
The proof is rather cumbersome.
This may appear rather wasteful, especially when n is close to m, but these terms only give a small contribution to our sum.
For explicit solutions, it may be necessary to have rather precise information about the amplitude φ.
A further complication arises from “selection'', which works rather differently from the other labels.