Lebesgue Spaces of Summable Functions

Decomposition of Lebesgue Spaces

Configuration spaces with summable labels

Let M be an n-manifold, and let A be a space with a partial sum behaving as an n-fold loop sum. We define the space C(M ;A) of configurations in M with summable labels in A via operad theory. Some examples are symmetric products, labelled configuration spaces, and spaces of rational curves. We show that C(In, ∂In;A) is an n-fold classifying space of C(In;A), and for n = 1 it is homeomorphic to ...

Spaces of Strongly Almost Summable Difference Sequences

The purpose of this paper is to introduce the concept of4m vλ strongly almost convergence with respect to a sequence of moduli and4m vλ Almost Statistical Convergence and give some relations between these two kinds of convergence. 2000 Mathematics Subject Classification: 40A05,40C05, 46A45.

Essential Supremum and Supremum of Summable Functions

Let D lR N , 0 < (D) < +1 and f : D ! lR is an arbitrary summable function. Then the function F() := R fx2D:f(x)g (f(x) ?) dd (2 lR) is continuous, non-negative, non-increasing, convex, and has almost everywhere the derivative F 0 () = ?f ]. Further on, it holds ess supf = supf 2 lR : F() > 0g, where ess supf denotes the essential supremum of f. These properties can be used for computing esssup...

Integral Representation of Linear Continuous Operators from the Space of Lebesgue-bochner Summable Functions into Any Banach Space.