Theorem 1. Let the countable abelian group G act nonsingularly and aperiodically on Lebesgue space (X, p.). Then for each finite subset A c G and e > 0 3 finite B c G and F tz X with [bF: bEB} disjoint and PKfl meAB a)F] > 1-e. Theorem 2. Every nonsingular action of a countable abelian group on a Lebesgue space is hyperfinite.

in this paper we obtain lower and upper estimates for the essential norms of generalized composition operators from weighted dirichlet spaces or bloch type spaces to $q_k$ type spaces.

Our main purpose of this article is to study the convergence and other related properties q-Bernstein-Kantorovich operators including shifted knots real positive numbers. We design Bernstein-Kantorovich generated by basic q-calculus. More precisely, we our new in space continuous functions Lebesgue space. obtain degree with help modulus continuity integral continuity. Furthermore, establish qua...

This paper concerns a family of weak parallelogram laws for Banach spaces. It is shown that the familiar Lebesgue spaces satisfy a range of these inequalities. Connections are made to basic geometric ideas, such as smoothness, convexity, and Pythagorean-type theorems. The results are applied to the linear prediction of random processes spanning a Banach space. In particular, theweak parallelogr...

For an arbitrary in nite-dimensional Banach space X, we construct examples of strongly-measurable X-valued Pettis integrable functions whose indefinite Pettis integrals are nowhere weakly di erentiable; thus, for these functions the Lebesgue Di erentiation Theorem fails rather spectacularly. We also relate the degree of nondi erentiability of the inde nite Pettis integral to the cotype of X, fr...

In this paper we show that for dictionaries with small coherence in a Hilbert space the Orthogonal Greedy Algorithm (OGA) performs almost as well as the best m−term approximation for all signals with sparsity almost as high as the best theoretically possible threshold s = 1 2 (M−1 + 1) by proving a Lebesgue-type inequality for arbitrary signals. On the other hand, we present an example of a dic...

Abstract In this short paper, I recall the history of dealing with lack compactness a sequence in case an unbounded domain and prove vanishing Lions-type result for Lebesgue-measurable functions. This lemma generalizes some results class Orlicz–Sobolev spaces. What matters here is behavior integral, not space.

We promote the concept of object directed computability in computational geometry in order to faithfully generalise the wellestablished theory of computability for real numbers and real functions. In object directed computability, a geometric object is computable if it is the effective limit of a sequence of finitary objects of the same type as the original object, thus allowing a quantitative ...