In Avid, there's a way to apply the same type of transition onto multiple cut points, either video or audio, all at the same time. You do it by putting an in point before the first cut and an out point after the last cut, and then click the transition button. A dialogue box comes up prompting you to adjust the parameters of the dissolve (duration, how many frames before cut, centered on cut, etc...) and it also gives you the option to check a box that says "apply to all transitions in-out" and another check box that allows you to "skip existing transitions". Check those boxes and click OK and if there are twenty cuts between your in and out points, it will put a dissolve on each one of those twenty cuts with those parameters you chose.
Is there any way to do this in Premiere? I am used to doing it the Avid way, and the only way I know how to apply multiple transition in Premiere so far seems to be to apply them one at at time, which is extremely tedious and slow.