简要目录如下:
1 Probability and Measure 1
Appendix1.A–Common Structure of the Proofs of Theorems 1.6 and 1.10 32
Appendix1.B–Extension of an Outer Measure to a Probability Measure 32
2 BorelMeasurability,Integration,andMathematical Expectations 37
Appendix2.A–Uniqueness of Characteristic Functions 61
3 Conditional Expectations 66
Appendix3.A–ProofofTheorem3.12 83
4 Distributions and Transformations 86
Appendix4.A–Tedious Derivations 104
Appendix4.B–Proof of Theorem4.4 106
5 The Multivariate Normal Distribution and Its Application to Statistical Inference 110
Appendix5.A–Proof of Theorem5.8 134
6 Modes of Convergence 137
Appendix6.A–Proof of the Uniform Weak Law of Large Numbers 164
Appendix6.B–Almost-Sure Convergence and Strong Laws of Large Numbers 167
Appendix6.C–Convergence of Characteristic Functions and Distributions 174
7 Dependent Laws of Large Numbers and Central Limit Theorems 179
Appendix7.A–Hilbert Spaces 199
8 Maximum Likelihood Theory 205
I ReviewofLinearAlgebra 229
II Miscellaneous Mathematics 283
III A Brief Review of ComplexAnalysis 298
IVTablesofCriticalValues 306
References 315
Index 317