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A method of integrating over difficult sets in Eⁿ by replacing the characteristic function of the set with a discontinuous integral has been used by Markov, Chandrasekhar, Melzak, and others. This thesis employs this method in some problems arising from random walks. A discussion of the difficulties encountered and suggestions for further study are included.doi:10.14288/1.0080449 fatcat:uv5ubiw6fne25ixgjhzvsd3vr4