Remark

— 1) The concepts so defined coincide, when T is locally compact, with the usual concepts. 2) After we have defined negligible sets, we will see that the locally negligible sets are indeed those whose germ, at every point of T, is the germ of a negligible set (No. 9, Cor. 2 of Prop. 14). 3) As in Chs. IV and V, the expression 'locally almost everywhere' will be synonymous with 'except on a locally negligible set'. 4) If $\theta$ is a complex measure, we shall say that a function (resp. a subset of T) is locally negligible for $\theta$ if it is so for the positive measure $|\theta|$.