Square-integrable Hausdorff-based measures and their products

In this book, we present a significant enlargement of the usual space of normalizable states belonging to Quantum systems with m degrees of freedom. Specically, we work in the relativistic Schrodinger setting of wave mechanics. In the above setting, usual quantum states belong to the Hilbert space L2(E,C), of Lebesgue square integrable functions (equivalence classes) defined upon a convenient m-dimensional Euclidean space E. By our approach, we will extend the range of possible quantum states E-based to a new class of measures upon the Euclidean space E, that shall contain the classic Lebesgue based function space L2, as well as the space of square integrable discrete measures and, more generally, all spaces L2 C(E, hd) of complex functions square integrable with respect to the normalized Hausdorff measures hd on E. We, then, define a product between two square integrable measures and show some applications to Quantum Mechanics.