内容简介: 数学 目录: Preface PART ONE Set Theory,Real Numbers,and Calculus 1 SET THEORY Biography: Georg Cantor 1.1 Basic Definitions and Properties 1.2 Functions and Sets 1.3 Equivalence of Sets; Countability 1.4 Algebras,σ-Algebras,and Monotone Classes
2 THE REAL NUMBER SYSTEM AND CALCULUS Biography: Georg Friedrich Bernhard Riemann 2.1 The Real Number System 2.2 Sequences of Real Numbers 2.3 Open and Closed Sets 2.4 Real-Valued Functions 2.5 The Cantor Set and Cantor Function 2.6 The Riemann Integral
PART TWO Measure,Integration,and DifFerentiation 3 LEBESGUE THEORY ON THE REAL LINE Biography: Emile Felix-Edouard-Justin Borel 3.1 Borel Measurable Functions and Borel Sets 3.2 Lebesgue Outer Measure 3.3 Further Pro ...
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