Chapter
1.5 Relationships between metrics
pp.：
48 – 72
1.6 Linearly invariant metrics
pp.：
72 – 99
2 The nature of limit theorems
pp.：
99 – 107
2.2 A generalization of the Lindeberg-Feller theorem
pp.：
107 – 117
2.1 The history of limit theorems
pp.：
107 – 107
2.3 Natural estimates of convergence rate in the central limit theorem
pp.：
117 – 129
2.4 Limit theorems as stability theorems
pp.：
129 – 140
2.5 One more mechanism forming the central limit theorem
pp.：
140 – 151
3 The normalization of random sequences
pp.：
151 – 159
3.2 The choice of constants under linear normalization
pp.：
159 – 169
3.1 General normalization problems
pp.：
159 – 159
4 Centers and scatters of random variables
pp.：
169 – 177
4.1 The definition and properties of index, centers and scatters
pp.：
177 – 177
4.2 An analog of the Chebyshev inequality
pp.：
177 – 185
4.3 Centers and scatters in the criteria of L-compactness
pp.：
185 – 190
4.4 Centers and scatters in the criteria of L-convergence of random sequences
pp.：
190 – 195
5 Classical theory of limit theorems for sums of independent random variables
pp.：
195 – 209
5.1 Reduced models
pp.：
209 – 209
5.2 Infinitely divisible laws
pp.：
209 – 216
5.3 Limit theorems of the classical theory
pp.：
216 – 221
5.4 The estimates of accuracy of approximations in limit theorems of the classical theory
pp.：
221 – 241
5.5 On completeness of classical theory
pp.：
241 – 263
6 Generalizations of the classical theory of summation of independent random variables
pp.：
263 – 273
6.2 Stability of compositions of distributions
pp.：
273 – 276
6.1 The history of the problem
pp.：
273 – 273
6.3 Limit theorems in a non-classical setting
pp.：
276 – 293
6.4 Limit theorems in the generalized summation scheme
pp.：
293 – 324
6.5 The method of metric distances
pp.：
324 – 354
6.6 Sums of non-independent random variables
pp.：
354 – 394
Bibliography
pp.：
394 – 411
Modern Theory of Summation of Random Variables
( Modern Probability and Statistics )
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