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Functional Operators. Volume I: Measures and Integrals

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Author(s): John Von Neumann
Publisher: Princeton
Year: 1950

Language: English

Title page
Foreword
Errata
I. Point Set Theory
II. Outer Measure
III. Measure
IV. Inner Measure
V. Invariance of Measure under Transformation
VI. Covering Theorems
VII. Non-measurable Sets
VIII. Lebesgue Intgeral
IX. Monotonic Functions
X. General Measure Functions and Outer Measures
l. Elementary Properties of Measure Functions
2. Outer Measure and Inner Measure
3. General Extension Theorems
4. Measure in Product Spaces
5. Examp1es of Measure Functions
XI. Properties of the General Integral
l. Bounded Variation and the Extension of Finite Measure Functions
2. Abso1ute Continuity and the Intgera1
3. Elementary Properties of the Integral
4. The Fubini Theorem and Re1ated Theorems