Bloom Filters- An Intro

Bloom Filters are quite simply put space-efficient, probabilistic data structures which help answer the question of set membership. From a mathematical lens say that you need to verify whether an element x belongs to a set A , if the Bloom Filter as a data structure returns true for x, what this means is that either x is definitely in the set A or it may not be in the set A. An implication that follow from this is that Bloom Filters are quite efficient at preprocessing and filtering out large lists, for further detailed set operations such as joins and intersections.