منابع مشابه
Covering theorems and Lebesgue integration
Abstract. This paper shows how the Lebesgue integral can be obtained as a Riemann sum and provides an extension of the Morse Covering Theorem to open sets. Let X be a finite dimensional normed space; let μ be a Radon measure on X and let Ω ⊆ X be a μ-measurable set. For λ ≥ 1, a μ-measurable set Sλ(a) ⊆ X is a λ-Morse set with tag a ∈ Sλ(a) if there is r > 0 such that B(a, r) ⊆ Sλ(a) ⊆ B(a, λr)...
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Let M be an oriented even-dimensional Riemannian manifold on which a discrete group Γ of orientation-preserving isometries acts freely, so that the quotientX = M/Γ is compact. We prove a vanishing theorem for a half-kernel of a Γ-invariant Dirac operator on a Γ-equivariant Clifford module overM , twisted by a sufficiently large power of a Γ-equivariant line bundle, whose curvature is non-degene...
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A branchpoint of a compactum X is a point which is the vertex of a simple triod in X. A surjective map /: X -» Y is said to cover the branchpoints of Y if each branchpoint in Y is the image of some branchpoint in X. If every map in a class % of maps on a class of compacta & covers the branchpoints of its image, then it is said that the branchpoint covering property holds for ff on 0. According ...
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We prove covering theorems for K, where K is the core model below the sharp for a strong cardinal, and give an application to stationary set reflection. 2000 Mathematics Subject Classification. 03. The author was supported in part by NSF grant DMS-0500799, and fellowships from the UCI mathematics department. This paper is the main part of the Ph.D. thesis ([2]). I would like to thank my advisor...
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In this paper we prove sharp covering theorems for nonconstant holomorphic functions f in the unit disk U. Theorem 1 asserts that if |f ′(0)| ≥ A|f(0)|, where A is a given number larger than 4, then f covers some annulus of the form r < |w| < Kr, where K = K(A) is a number depending on A. The theorem is sharp; extremals are furnished by universal covering maps from U onto the plane minus a doub...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1926
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1926-04207-5