This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorffs classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for references to other sources. Along the lines of Hausdorffs initial work (1st ed., 1914), measure and integration theory is also included here as the third fundamental part of contemporary mathematics. The material about sets and numbers is placed in Volume 1 and the material about functions and measures is placed in Volume 2.

ContentsHistorical foreword on the centenary after Felix Hausdorffs classic Set TheoryFundamentals of the theory of functionsFundamentals of the measure theoryHistorical notes on the Riesz Radon Frechet problem of characterization of Radon integrals as linear functionals

Alexander V. Mikhalev,Timofey V. Rodionov andValeriy K. Zakharov, Lomonosov Moscow State University, Russia.