Bloom filter like data structure supporting iteration


I am wondering whether there exists a data structure similiar to a bloom filter in the sense that it is an approximate finite set representation (allows for false positives, but no false negatives) and supports:

  • constant time complexity union of two sets
  • constant time complexity insertion of an element

but also allows for efficient iteration over the approximate elements in the set, i.e. iterate over all elements that are either actually in the set or false positives with a time complexity that is linear in the number of elements in the set