0000000000643057
AUTHOR
Corneliu Constantinescu
showing 5 related works from this author
Suggestions to the Reader
1998
Each section of the book consists of two parts that have different goals. The first part, namely the text itself, is systematically developed. It consists of definitions and proven assertions assembled in an organized fashion and with no significant gaps for the reader to fill. All propositions and theorems, unless ready consequences of definitions and previously proven assertions, are proved in detail.
The Classical Theory of Real Functions
1998
The first class of real functions we deal with in this chapter is the class of functions of locally finite variation. These functions are closely related to the real measures on B. Exploiting this connection would allow us to obtain the properties of these functions from the general results in Chapter 4. But the path we follow here is a more direct one which applies the theory of vector lattices. The link with the measures on B will be established in the next section.
The Radon-Nikodym Theorem. Duality
1998
The band in M( ℜ) generated by a particular real measure μ can be characterized in various ways.
Elementary Integration Theory
1998
This section begins with the definitions and elementary properties of real and extended-real functions.
Lp-Spaces
1998
For (X, ℜ, μ) a positive measure space, it has already been noted that μ - a.e. equality is an equivalence relation, and the relation ≤ μ-a.e. a preorder, on.This section studies the structure of the equivalence classes into which μ-a,e. equality partitions.Since the set X/X( ℜ) is always u-null (2.7.7 a)), only the function values on the set X(ℜ) have any significance when equivalence classes are formed: whether we form equivalence classes by partitioning or by partitioningX(ℜ) the resulting structures will be isomorphic. Nevertheless, it is natural to allow functions on an arbitrary X ⊃ X(ℜ). Our choice is to form μ-equivalence classes by partitioning the set X(ℜ). For arbitrary X ⊃ X(ℜ),…