A new class of transport distances between measures

A new class of transport distances between measures

We introduce a new class of distances between nonnegative Radon measures in Rd . They are modeled on the dynamical characterization of the Kantorovich-RubinsteinWasserstein distances proposed by BENAMOU-BRENIER [7] and provide a wide family interpolating between the Wasserstein and the homogeneousW−1,p γ -Sobolev distances. From the point of view of optimal transport theory, these distances min...

Comparison of distances between measures

The problem of optimal transportation between a set of sources and a set of wells has become recently the object of new mathematical models generalizing the Monge-Kantorovich problem. These models are more realistic as they predict the observed branching structure of communication networks. They also define new distances between measures. The question arises of how these distances compare to th...

A new class of entanglement measures

Abstract We introduce new entanglement measures on the set of density operators on tensor product Hilbert spaces. These measures are based on the greatest cross norm on the tensor product of the sets of trace class operators on Hilbert space. We show that they satisfy the basic requirements on entanglement measures discussed in the literature, including convexity, invariance under local unitary...

A new class of fuzzy poverty measures

In this paper, we introduce and analyze a class of fuzzy poverty measures based on exponential means. Since poverty is a vague notion, individuals should not be classified in poor or non-poor. In our proposal, we have associated a degree of poverty to each income through a fuzzy membership function. We have extended normalized gaps from the classical approach, where poverty is a dichotomous not...

A New Class of Banach Sequence Spaces