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Preliminaries of Real Functions

In: Value Distribution of Meromorphic Functions

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  • Jianhua Zheng

    (Tsinghua University, Department of Mathematical Sciences)

Abstract

The various characteristics of meromorphic functions are main tool in the study of value distribution of meromorphic functions this book will introduce. They are real-valued functions defined on the positive real axis. In this chapter, we discuss certain properties of such real functions for application in later chapters. We begin with the order and the lower order of such functions which include the proximate order and the type function. We discuss the existence of the Pólya peak sequence. Also, we identify a sequence of positive numbers with some of the Pólya peak properties. We mainly introduce a result of Edrei and Fuchs for the regularity, thereby, improving the lemma of Borel and quasi-invariance of inequalities of two real functions under differentiation and integration. Finally, we exhibit the Green formula and collect several integral inequalities.

Suggested Citation

  • Jianhua Zheng, 2010. "Preliminaries of Real Functions," Springer Books, in: Value Distribution of Meromorphic Functions, chapter 0, pages 1-23, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-12909-4_1
    DOI: 10.1007/978-3-642-12909-4_1
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