A double is, in fact, an object, so you should probably just use TIntObjectHashMap<double>.
Try their containsKey method. If the value comes back 0, use that method to check if the map contains the key - if it does, then the key's value really is 0. If it doesn't, then the key is not set.
fastutil is all ways better than Trove. There is IntSortedSet interface with firstInt() and lastInt() methods.