[ with short note at end ] We consider a nonlocal analogue of the Fisher-KPP equation. We do not assume that the Borel-measure for the convolution is absolutely continuous. In order to show the main result, we modify a recursive method for abstract monotone discrete dynamical systems by Weinberger. We note that the monotone semiflow generated by the equation does not have compactness with respect to the compact-open topology. At the end, we propose a discrete Schrodinger model that describes the measurement process. https://doi.org/10.5281/zenodo.3405367 https://doi.org/10.48550/arXiv.0807.3612