Isometric embeddings of finite metric spaces

It is proved that there exists a metric on a Cantor set such that any finite metric space whose diameter does not exceed 1 and the number of points does not exceed n can be isometrically embedded into it. It is also proved that for any m, n a N there exists a Cantor set in R (m) that isometrically contains all finite metric spaces which can be embedded into R (m) , contain at most n points, and have the diameter at most 1. The latter result is proved for a wide class of metrics on R (m) and, in particular, for the Euclidean metric.