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
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