  Phenomena with a constrained sample space appear frequently in practice. This
is the case e.g. with strictly positive data and with compositional data, like
percentages and the like. If the natural measure of difference is not the
absolute one, it is possible to use simple algebraic properties to show that it
is more convenient to work with a geometry that is not the usual Euclidean
geometry in real space, and with a measure which is not the usual Lebesgue
measure, leading to alternative models which better fit the phenomenon under
study. The general approach is presented and illustrated both on the positive
real line and on the D-part simplex.
