local maxima feller says that unimodal distribution is a distribution function that is convex up to the mode and concave beyond it thus it may have density taking maximal values on an interval say uniform distribution on in this case all points in are local maxima or there aren't any if we consider strict 'peaks' only therefore i suggest a more general definition of a unimodal function a function whose local maxima make up an interval moreover it might be worth replacing ' this allows for the possibility of a non zero probability for x m ' with ' in this case the distribution may have density everywhere except possibly m this allows for the possibility of a non zero probability for x m '