I The Case of a Single Experiment and Finite Sample Space.- 1. Basic facts. Maximal and extremal families.- 2. Induced maximal and extremal families.- 3. Convexity, maximal and extremal families.

- 4. Some examples.- II Simple Repetitive Structures of Product Type. Discrete Sample Spaces.- 0. Conditional independence.- 1. Preliminaries.

Notation.- 2. Notions of sufficiency.- 3. Maximal and extremal families.- 4. Limit theorems for maximal and extremal families.- 5.

The topology of$$\left( {\mathop{{\dot{U}}}\limits_{n} {{y}_{n}}} \right)UM.$$Boltzmann laws.- 6. Integral representation of M.- 7. Construction of maximal and extremal families.- 8. On the triviality of the tail ?-algebra of a Markov chain.

- 9. Examples of extremal families.- 10. Bibliographical notes.- III Repetitive Structures of Power Type. Discrete Sample Spaces.- 0. Basic facts about Abelian semigroups.

- 1. Extremal families for semigroup statistics.- 2. General exponential families.- 3. The classical case.zd-valued statistics.- 4.

Maximum likelihood estimation in general exponential families.- 5. Examples of general exponential families.- 6. Bibliographical notes.- IV General Repetitive Structures of Polish Spaces. Projective Statistical Fields.- 0.

Probability measures on Polish spaces.- 1. Projective systems of Polish spaces and Markov kernels.- 2. Projective statistical fields.- 3. Canonical projective statistical fields on repetitive structures.- 4.

Limit theorems for maximal and extremal families on repetitive structures.- 5. Poisson Models.- 6. Exponential Families.- 7. Examples from continuous time stochastic processes.- 8.

Linear normal models.- 9. The Rasch model for item analysis.- 10. Bibliographical notes.- Literature.