A sigma-algebra and a concept of limit for bodies

Recent developments in mechanics of continua (the search for optimal shapes of bodies, homogenization theory, the study of the trabecular structure of bones, the dynamics of immiscible mixtures, etc.) render some of the intro ductory axioms of continuum mechanics inadequate. Not only does one need to give meaning to the join and meet of two bodies, but also to extend the co nsequent algebra so as to encompass the result of a countable sequence of o perations of join or meet; and one should also be able to define the limit of a sequence of bodies. To achieve this goal we propose here to define a b ody ab initio through the assignment of a probability measure d pi. We real ize that pi leaves, generally, too much of the texture of the body unspecif ied; to make up for this deficiency, we suggest the use of appropriate text ure measures, reminescent of Tartar's H-measurcs.(9).