In this book, I attempt to reach two goals. The first is purely mathematical: to clarify some of the basic concepts of probability theory. The second goal is physical: to clarify the methods to be used when handling the information brought by measurements, in order to understand how accurate are the predictions we may wish to make.
Probability theory is solidly based on Kolmogorov axioms, and there is no problem when treating discrete probabilities. But I am very unhappy with the usual way of extending the theory to continuous probability distributions. In this text, I introduce the notion of ‘volumetric probability’ different from the more usual notion of ‘probability density’. I claim that some of the more basic problems of the theory of continuous probability distributions can only ne solved within this framework, and that many of the well known ‘paradoxes’ of the theory are fundamental misunderstandings, that I try to clarify.

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