EN
CONTENTS
Introduction..............................................................................................................5
1. Preliminaries........................................................................................................6
1.0. Measurable, probabilistic, and statistical spaces..............................................6
1.1. Transition functions..........................................................................................6
1.2. Linear space of P-bounded measurable real functions....................................8
1.3. Almost transition functions................................................................................9
2. Concrete categories of measurable, probabilistic, and statistical spaces..........14
3. Categories connected with transition functions..................................................16
3.1. Category $Mes_{trans}$.................................................................................16
3.2. Category $St_{trans}$....................................................................................19
3.3. Category $St_{dist}$......................................................................................20
3.4. Categories of indexed statistical spaces.........................................................23
4. Categories connected with almost transition functions......................................23
Final remarks.........................................................................................................27
References............................................................................................................28