Measure and integration: Comparison of old and new procedures (Q1291144)

The author summarizes the outer and inner extension theories on the level of set functions and presents main theorems on the level of functionals. In particular, sequential and nonsequential versions of the Daniell-Stone theorem are studied covering the topological theories of Bourbaki on locally compact spaces as well as of Schwartz on arbitrary Hausdorff spaces. Unfortunately, the recent book ``Integration -- a functional approach'' (1998; Zbl 0901.28001) by \textit{K. Bichteler} on related topics based on the notions Daniell mean and Jordan mean is even not mentioned.