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

This was causing great problems for probabilists, until Skorohod realized that one could change the metric since two people can walk on the paths of f and g and stay always close to each other if they are willing to adjust their speed a little.

Ampelmann and his friend are using Skorohod metric to stay close at all times.