Irregularities of continuous distributions
This paper deals with a continuous analogon to irregularities of point distributions. If a continuous fonction where is a compact body, is interpreted as a particle’s movement in time, then the discrepancy measures the difference between the particle’s stay in a proper subset and the volume of the subset. The essential part of this paper is to give lower bounds for the discrepancy in terms of the arc length of , . Furthermore it is shown that these estimates are the best possible despite of...