Abstract
In this chapter, the concept of a measure is defined, and some of its basic properties are established. We then proceed with the introduction of an outer measure, study its relationship to the underlying measure, and determine the class of sets measurable with respect to the outer measure. These results are used as a basis toward obtaining an extension of a given measure from a field to the σ-field generated by this field. Next, by means of a measure, a class of point real-valued functions is defined, and their basic properties are studied. Finally, it is shown that any nondecreasing right-continuous function induces a unique measure in the Borel real line.
Published Version
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