On the magnitude of metric spaces -

Abstract

In this thesis, we consider the magnitude of finite metric spaces and that of compact subsets of Euclidean spaces. We will consider an extension of the definition of finite spaces to compact metric spaces using three different approaches. Our contribution to this work consists in giving new proofs for the magnitude of segments and general compact sets of R. In addition, we give a presentation of the proof that the magnitude dimension of compact subsets of Euclidean space is equal to the Minkowski dimension.