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)...
متن کاملVanishing Theorems on Covering Manifolds
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...
متن کاملCurvature in Abstract Boundary Singularity Theorems
The abstract boundary construction of Scott and Szekeres is a general and flexible way to define singularities in General Relativity. The abstract boundary construction also proves of great utility when applied to questions about more general boundary features of space-time. Within this construction an essential singularity is a non-regular boundary point which is accessible by a curve of inter...
متن کاملBranchpoint Covering Theorems for Confluent and Weakly Confluent Maps
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 ...
متن کاملA Finite Covering Tree for Analysing Entropic Broadcast Protocols (Abstract)
For general broadcast protocols, the natural generalization of the Karp and Miller procedure does not terminate; even the problem of deciding if a broadcast protocol may exhibit an infinite behavior is undecidable [4]. We define a subclass of broadcast protocols, called entropic broadcast protocols, which "contains" the MESI protocol, and we prove that the Generalized Karp and Miller procedure ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1963
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-52-2-205-207