It is argued that a reformulation of classical measure theory is necessary if the theory is to accurately describe measurements of physical phenomena. The postulates of a generalized measure theory are given and the fundamentals of this theory are developed, and the reader is introduced to some open questions and possible applications. Specifically, generalized measure spaces and integration theory are considered, the partial order structure is studied, and applications to hidden variables and the logic of quantum mechanics are given.

Quantum theory has played a significant role in modern philosophy both as a source of metaphysical ideas and as an important example of a 'scientific revolution'. In spite of the sixty or so years that have elapsed since its invention, a long lasting controversy concerning the interpretation and meaning of quantum theory prevails. Almost all authors, however, seem to agree on one major point, namely, that there could be no interpretation of this theory which is both realistic and local. ;The (...) purpose of this thesis is to demonstrate that this premiss is false and that a realistic, local and deterministic interpretation of quantum theory does exist, provided that we extend the classical concept of probability. ;In order to establish this a 'quasi classical' probability theory is developed based on some non Lebesgue measurable 'events', which is then applied to account for spin-statistics. Finally I note how this model reflects on the problems of physical realism, locality, the status of probability theory and the philosophical foundations of mathematics. (shrink)

A deterministic model that accounts for the statistical behavior of random samples of identical particles is presented. The model is based on some nonmeasurable distribution of spin values in all directions. The mathematical existence of such distributions is proved by set-theoretical techniques, and the relation between these distributions and observed frequencies is explored within an appropriate extension of probability theory. The relation between quantum mechanics and the model is specified. The model is shown to be consistent with known polarization phenomena (...) and the existence of macroscopic magnetism. Finally.. (shrink)