Nécessité de l’étude de la fonction diastolique dans l’évaluation de la cardiotoxicité des traitements anticancéreux par gamma-angiographie

This chapter discusses extensive ultraproducts and Haar measure. A Haar measure is one which is positive on nonempty open sets, finite on compact sets, regular, and invariant under translation. Real-valued Haar measures exist for topological groups which are locally-compact; but for the non-locally compact groups there are, in a sense, not enough real numbers for us to be able to give positive real measures to all the deserving sets. A translation invariant measure which takes values in an ultrapower of the reals is constructed. Ultrapower-bounded measures are given to sets which have compact intersections with sufficiently many locally compact subgroups of the given topological group. A preliminary section is given to the introduction of the extensive ultraproduct and to the definition of infinite sums. The real-valued Haar measure on a given locally compact group is unique only to within a multiplicative constant.