Von Mises Probability and Hilbert Space

There are two major theories of probability, one due to von Mises and the other due to Kolmogorov. The first requires the existence of a collective before probabilities can be defined. Its motivation is physical. The second postulates a probability space which is purely mathematical. It makes probability a branch of mathematics. We show that von Mises' theory is more appropriate to application in quantum theory. Kolomogorov's theory can lead to paradoxical results.