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Geometric Integration Theory

Hassler Whitney

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Princeton University Press img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Mathematik

Beschreibung

A complete theory of integration as it appears in geometric and physical problems must include integration over oriented r-dimensional domains in n-space; both the integrand and the domain may be variable. This is the primary subject matter of the present book, designed to bring out the underlying geometric and analytic ideas and to give clear and complete proofs of the basic theorems.

Originally published in 1957.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

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Schlagwörter

Interior product, Vector space, Differentiable manifold, Exact differential, Improper integral, Radon–Nikodym theorem, Differential form, Stone–Weierstrass theorem, Cartesian product, Function (mathematics), Unit vector, Bounded variation, Lebesgue integration, Partition of unity, Existence theorem, Measurable function, Summation, Partial derivative, Smoothness, Banach space, Dot product, Antiderivative, Absolute continuity, Special case, Step function, Coordinate system, Theorem, Betti number, Linear function, Basis (linear algebra), Infimum and supremum, Total variation, Upper and lower bounds, Algebraic topology (object), Linear extension, Linear map, Linear space (geometry), Projection (linear algebra), Skew-symmetric matrix, Rademacher's theorem, Characterization (mathematics), Grassmannian, Lebesgue measure, Riemannian manifold, Metric space, Simply connected space, Cohomology, Open set, Affine coordinate system, Cauchy sequence, Stokes' theorem, Euclidean space, Orthogonal complement, Dense set, Fubini's theorem, Compact space, Permutation, Exterior (topology), Lipschitz continuity, Bivector, Exterior algebra, Intersection (set theory), Bounded set (topological vector space), Maximal set, Borel set, Limit point, Complete metric space, N-vector, Subset, Affine space