1 Preliminaries of Real Functions 1
1.1 Functions of a Real Variable 1
1.1.1 The Order and Lower Order of a Real Function 1
1.1.2 The Pólya Peak Sequence of a Real Function 4
1.1.3 The Regularity of a Real Function 8
1.1.4 Quasi-invariance of Inequalities 14
1.2 Integral Formula and Integral Inequalities 19
1.2.1 The Green Formula for Functions with Two Real Variables 19
1.2.2 Several Integral Inequalities 20
References 23
2 Characteristics of a Meromorphic Function 25
2.1 Nevanlinna's Characteristic in a Domain 26
2.2 Nevanlinna's Characteristic in an Angle 47
2.3 Tsuji's Characteristic 58
2.4 Ahlfors-Shimizu's Characteristic 66
2.5 Estimates of the Error Terms 77
2.6 Characteristic of Derivative of a Meromorphic Function 86
2.7 Meromorphic Functions in an Angular Domain 93
2.8 Deficiency and Deficient Values 103
2.9 Uniqueness of Meromorphic Functions Related to Some Angular Domains 110
References 120
3 T Directions of a Meromorphic Function 123
3.1 Notation and Existence of T Directions 124
3.2 T Directions Dealing with Small Functions 130
3.3 Connection Among T Directions and Other Directions 134
3.4 Singular Directions Dealing with Derivatives 146
3.5 The Common T Directions of a Meromorphic Function and Its Derivatives 151
3.6 Distribution of the Julia,Borel Directions and T Directions 163
3.7 Singular Directions of Meromorphic Solutions of Some Equations 166
3.8 Value Distribution of Algebroid Functions 178
References 181
4 Argument Distribution and Deficient Values 185
4.1 Deficient Values and T Directions 186
4.2 Retrospection 202
References 205
5 Meromorphic Functions with Radially Distributed Values 207
5.1 Growth of Such Meromorphic Functions 208
5.2 Growth of Such Meromorphic Functions with Finite Lower Order 215
5.3 Retrospection 222
References 228
6 Singular Values of Meromorphic Functions 229
6.1 Riemann Surfaces and Singularities 230
6.2 Density of Singularities 241
6.3 Meromorphic Functions of Bounded Type 252
References 265
7 The Potential Theory in Value Distribution 267
7.1 Signed Measure and Distributions 268
7.2 δ-Subharmonic Functions 270
7.2.1 Basic Results Concerning δ-Subharrnonic Functions 271
7.2.2 Normality of Family of δ-Subharmonic Functions 275
7.2.3 The Nevanlinna Theory of δ-Subharmonic Functions 285
7.3 Eremenko's Proof of the Nevanlinna Conjecture 292
References 305
Index 307