Published by De Gruyter

Sets, Functions, Measures

Volumes

Book 2018

Volume 1 Fundamentals of Set and Number Theory

Valeriy K. Zakharov, Timofey V. Rodionov

Volume 68/1 in the series De Gruyter Studies in Mathematics

More Cite

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
Fundamentals of the theory of classes, sets, and numbers
Characterization of all natural models of Neumann – Bernays – Godel and Zermelo – Fraenkel set theories
Local theory of sets as a foundation for category theory and its connection with the Zermelo – Fraenkel set theory
Compactness theorem for generalized second-order language

DOI:: https://doi.org/10.1515/9783110550948
ISBN:: 9783110550948
ISBN:: 9783110550214
ISBN:: 9783110550085
Subject:: Mathematics
Subject:: Logic and Set Theory
Subject:: Analysis
Publisher:: De Gruyter

Book 2018

Volume 2 Fundamentals of Functions and Measure Theory

Valeriy K. Zakharov, Timofey V. Rodionov, Alexander V. Mikhalev

Volume 68/2 in the series De Gruyter Studies in Mathematics

More Cite

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

DOI:: https://doi.org/10.1515/9783110550962
ISBN:: 9783110550962
ISBN:: 9783110550221
ISBN:: 9783110550092
Subject:: Mathematics
Subject:: Logic and Set Theory
Subject:: Analysis
Publisher:: De Gruyter