During the last 20 years, as collocated fully-sampled data have become more common, several approaches to cokriging multivariate regionalized data sets have been published in Mathematical Geology. However, most case studies still today use univariate kriging of each individual compo- nent, a practice which may lead to inconsistencies: interpolated results may not honour constraints inherent to the data set, like compositions or probability vectors with negative components, or not summing up to one, or indicators with order relation violations. But, if the sample space of the observed vectors admits a meaningful Euclidean structure, one can find a clean solution to these inconsistencies. Given that this structure redefines the linear operations, it implies new linear functions, and criteria to compute differences between vectors. Following the argument, a simple cokriging estimator may be defined, which ends up being best, linear and unbiased, with the new meanings of these words. Fortunately, existing software is fully useful for this "new" co-kriging estimator, because it becomes the classical one applied to the coordinates of the regionalized vector with respect to an arbitrary vector basis of the Euclidean space. As an example, the Aitchison geometry of the simplex may be used to interpolate compositions and disjunctive indicators, offering a clearer way to model covariance structures, and results which never presen order relation violations--as typically occurs in conventional indicator kriging--.
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