We collect here a brief account of the various mathematical conventions used throughout this work, and discuss some basic mathematical issues that arise in probability theory. Careless notation has led to so many erroneous results in the recent literature that we need to find rules of notation and terminology that make it as difficult as possible to commit such errors.

A mathematical notation, like a language, is not an end in itself but only a communication device. Its purpose is best served if the notation, like the language, is allowed to evolve with use. This evolution usually takes the form of abbreviations for whatever expressions recur often, and reducing the number of symbols when their meaning can be read from the context.

But a living, changing language still needs a kind of safe harbor in the form of a fixed set of rules of grammar and orthography, hidden away in a dictionary for use when ambiguities threaten. Likewise, probability theory needs a fixed set of normative rules on which we can fall back in case of doubt. We state here our formal rules of notation and logical hierarchy; all chapters from Chapter 3 on start with these standard forms, and evolve from them. A notation which is so convenient that it is almost a necessity in one chapter might be only confusing in the next; so each separate topic must be allowed its own independent evolution from the standard beginning.