Distance Between Sets - A survey

TL;DR

This survey reviews various notions of distance between sets in metric and measure spaces, covering definitions, classifications, and applications across theoretical and practical domains.

Contribution

It provides a comprehensive overview of set distances, including classifications and applications, consolidating existing knowledge in a unified survey.

Findings

Summarizes key distance functions and their properties.

Classifies different notions of set distances.

Highlights diverse applications across fields.

Abstract

The purpose of this paper is to give a survey on the notions of distance between subsets either of a metric space or of a measure space, including definitions, a classification, and a discussion of the best-known distance functions, which is followed by a review on applications used in many areas of knowledge, ranging from theoretical to practical applications.