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.