Quantum Mechanical Probabilities Not Restricted to a Moment of Time

A theoretical aspect of quantum mechanical probabilities is studied. In particular, it is investigated whether quantum mechanical probabilities can be defined for alternatives which are not restricted to a moment of time. Firstly the meaning and the status of this investigation in quantum mechanics are explained. Secondly a general framework is constructed within which we make the investigation. Thirdly a necessary mathematical tool is reviewed and extended. Lastly the general framework is applied to concrete examples with the help of the mathematical tool. Examples of alternatives are found which are not restricted to a moment of time and for which quantum mechanical probabilities can be defined with clear measurement theoretical meanings if an initial condition of the particle belongs to a specific class. (This is the doctoral thesis of the author.