Preface to the English edition xiii Basic notations xv Introduction
xvii amPl'ER 1. Mathenatical Geology and the Developnent of
Geological Sciences 1 1. 1 Introduction 1 1. 2 Developnent of
geology and the change of paradigms 2 1. 3 Organization of the
mediun and typical structures 8 1. 4 statement of the problem: the
role of models in the search for solutions 14 1. 5 Mathematical
geology and its developnent 19 References 23 amPTER II. Probability
Space and Randan Variables 29 11. 1 Introduction 29 11. 2 Discrete
space of elementary events 29 11. 2. 1 Probability space 30 II. 2 *
2 Randan variabl es 33 11. 3 Kolroogorov's axian; The Lebesgue
integral 35 II. 3. 1 Probability space and randan variables 36 I 1.
3. 2 The Lebesgue integral 40 II. 3. 3 Nunerical characteristics of
raman variables 44 II. 4 ~les of distributions of randan variables
46 II. 4. 1 Discrete distributions 46 II. 4. 2 Absolutely
continuous distributions 51 II. 5 Vector randan variables 58 II. 5.
1 Product of probability spaces 58 II. 5. 2 Distribution of vector
randan variables 60 II. 5. 3 Olaracteristics of vector randan
variables 65 11. 5. 4 Exanples of distributions of vector raman
variabl es 69 II . 5. 5 Conditional distributions with respect to
randan variables 81 II. 6 Transfomations of randan variables 90 11.
6. 1 Linear transfomations 91 II. 6. 2 Sane non-linear
transfomations 95 11. 6.
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