The following two step functions, f and g on [0,1] say, look alike but they are not close in standard the uniform metric

This was causing great problems for probabilists, until Skorohod in his mid 20's realized that one should change the metric since two people can walk on their paths and stay close together if they are willing to adjust their speed a little.

Ampelmann and his friend are using Skorohod metric to stay close at all times on these two paths.