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Measure theory is a classical area of mathematics born more than two thousand years ago. Nowadays it continues intensive development and has fruitful connections with most other fields of mathematics as well as important applications in physics. This book gives an exposition of the foundations of modern measure theory and offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the basic course (the material of this level corresponds to a variety of special courses), and, finally, more specialized topics partly covered by more than 850 exercises. Volume 1 (Chapters 1-5) is devoted to the classical theory of measure and integral. Whereas the first volume presents the ideas that go back mainly to Lebesgue, the second volume (Chapters 6-10) is to a large extent the result of the later development up to the recent years. The central subjects of Volume 2 are: transformations of measures, conditional measures, and weak convergence of measures. These three topics are closely interwoven and form the heart of modern measure theory.
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Subject categories
- Academic > Mathematics > Calculus > Integrals, Generalized
- Academic > Mathematics > General > Mathematics
- Academic > Mathematics > General > Mathematics, Greek
- Academic > Mathematics > Analysis
- Academic > Physics > Mathematical physics
- Academic > Physics > Matrices
- Academic > Physics > Atomic physics
- Mathematics
ISBNs
3540345140
9783540345138
9783540345145