  The local Minkowski tensors are valuations on the space of convex bodies in
Euclidean space with values in a space of tensor measures. They generalize at
the same time the intrinsic volumes, the curvature measures and the isometry
covariant Minkowski tensors that were introduced by McMullen and characterized
by Alesker. In analogy to the characterization theorems of Hadwiger and
Alesker, we give here a complete classification of all locally defined tensor
measures on convex bodies that share with the local Minkowski tensors the basic
geometric properties of isometry covariance and weak continuity.
