منابع مشابه
The distributional Denjoy integral
Let f be a distribution (generalised function) on the real line. If there is a continuous function F with real limits at infinity such that F ′ = f (distributional derivative) then the distributional integral of f is defined as ∫ ∞ −∞ f = F (∞)−F (−∞). It is shown that this simple definition gives an integral that includes the Lebesgue and Henstock–Kurzweil integrals. The Alexiewicz norm leads ...
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We consider effective versions of two classical theorems, the Lebesgue density theorem and the Denjoy-Young-Saks theorem. For the first, we show that a Martin-Löf random real z ∈ [0, 1] is Turing incomplete if and only if every effectively closed class C ⊆ [0, 1] containing z has positive density at z. Under the stronger assumption that z is not LR-hard, we show that every such class has densit...
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This paper investigates the existence of Denjoy minimal sets and, more generally, strictly ergodic sets in the dynamics of iterated homeomorphisms. It is shown that for the full two-shift, the collection of such invariant sets with the weak topology contains topological balls of all finite dimensions. One implication is an analogous result that holds for diffeomorphisms with transverse homoclin...
متن کاملThe Denjoy alternative for computable functions
The Denjoy-Young-Saks Theorem from classical analysis states that for an arbitrary function f : R → R, the Denjoy alternative holds outside a null set. This means that for almost every real x, either the derivative of f exists at x, or the derivative fails to exist in the worst possible way: the limit superior of the slopes around x equals +∞, and the limit inferior −∞. Algorithmic randomness a...
متن کاملDenjoy Minimal Sets Are Far from Affine
Not every Cantor set can arise as the minimal set for a C 1 diieomor-phism of the circle. For example, D. McDuu has shown that the usual \middle thirds" Cantor set cannot arise this way. In this note we exclude a suitable neighborhood of the class of aane Cantor sets.
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ژورنال
عنوان ژورنال: Topology
سال: 1989
ISSN: 0040-9383
DOI: 10.1016/0040-9383(89)90032-3