A STUDY ON A COMPARISON OF CATEGORY AND LEBESGUE MEASURE

Author (s) : Dr.P.SOWMIYA, A.KAVITHA, MRS.V.NANDHINI

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Abstract :
The notions of category and Lebesgue measure are commonly used to describe the size of a set of real numbers (or of a subset of Rn). Although cardinality is also a measure of the size of a set, category and measure are often the more important gauges of size when studying properties of classes of real functions, such as the space of continuous functions or the space of derivatives. Category can also be easily extended to complete metric spaces other than the real line, such as the space of continuous functions on a compact interval under uniform convergence: Thus through the study of Category one can study sets of functions as well as sets of real numbers. The following is a comparison of these two notions as well as a survey of useful results.

Keywords : Measure set, Measurable,Outer Measure

Conference Date : 13/11/2020

Pages : 98

Paper ID : 20098