Alexander V. Mikhalev & Timofey V. Rodionov 
Fundamentals of Functions and Measure Theory [PDF ebook] 

This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff’s 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 Hausdorff’s 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. Contents Historical foreword on the centenary after Felix Hausdorff’s classic Set Theory Fundamentals of the theory of functions Fundamentals of the measure theory Historical notes on the Riesz – Radon – Frechet problem of characterization of Radon integrals as linear functionals