Book Description:
This treatment of geometric integration theory consists of an introduction to classical theory, a postulational approach to general theory, and a section on Lebesgue theory. Covers the theory of the Riemann integral; abstract integration theory; some relations between chains and functions; Lipschitz mappings; chains and additive set functions, more. 1957 edition
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Description:
This textbook introduces geometric measure theory through the notion of currents. Currents, continuous linear functionals on spaces of differential forms, are a natural language in which to formulate types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis.
The text provides considerable background for the student and discusses techniques that are applicable to complex geometry, partial differential equations, harmonic analysis, differential geometry, and many other parts of mathematics. Topics include the deformation theorem, the area and coareas formulas, the compactness theorem, the slicing theorem and applications to minimal surfaces.
Motivating key ideas with examples and figures, Geometric Integration Theory is a comprehensive introduction ideal for both self-study and for use in the classroom
The text provides considerable background for the student and discusses techniques that are applicable to complex geometry, partial differential equations, harmonic analysis, differential geometry, and many other parts of mathematics. Topics include the deformation theorem, the area and coareas formulas, the compactness theorem, the slicing theorem and applications to minimal surfaces.
Motivating key ideas with examples and figures, Geometric Integration Theory is a comprehensive introduction ideal for both self-study and for use in the classroom
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Integration Theory: With Special Attention to Vector Measures (Lecture Notes in Mathematics)
by Klaus Bichteler
by Klaus Bichteler
password: twilightzone
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Lebesgue Integration on Euclidean Space (Revised Ed.) (Jones and Bartlett Books in Mathematics)
by Frank Jones
by Frank Jones
Book Description:
Lebesgue Integration on Euclidean Space contains a concrete, intuitive, and patient derivation of Lebesgue measure and integration on Rn. Throughout the text, many exercises are incorporated, enabling students to apply new ideas immediately. Jones strives to present a slow introduction to Lebesgue integration by dealing with n-dimensional spaces from the outset. In addition, the text provides students a through treatment of Fourier analysis, while holistically preparing students to become "workers" in real analysis.
Lebesgue Integration on Euclidean Space contains a concrete, intuitive, and patient derivation of Lebesgue measure and integration on Rn. Throughout the text, many exercises are incorporated, enabling students to apply new ideas immediately. Jones strives to present a slow introduction to Lebesgue integration by dealing with n-dimensional spaces from the outset. In addition, the text provides students a through treatment of Fourier analysis, while holistically preparing students to become "workers" in real analysis.
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