An example of a measure "m" that is σ-finite but not moderated is given by as follows. The topological space "X" has as underlying set the subset of the real plane given by the "y"-axis of points (0,"y") together with the points (1/"n","m"/"n"2) with "m","n" positive integers. The topology is given as follows. The single points (1/"n","m"/"n"2) are all open sets. A base of neighborhoods of the point (0,"y") is given by wedges consisting of all points in "X" of the form ("u","v") with |"v" − "y"| ≤ |"u"| ≤ 1/"n" for a positive integer "n". This space "X" is locally compact. The measure "m" is given by letting the "y"-axis have measure 0 and letting the point (1/"n","m"/"n"2) have measure 1/"n"3. This measure is inner regular and locally finite, but is not outer regular as any open set containing the "y"-axis has measure infinity. In particular the "y"-axis has "m"-measure 0 but "M"-measure infinity.