Abstract: Pointwise weak laws of large numbers and weak laws of large numbers in the norm topology of D 0, 1 are shown to be equivalent under the condition （B）. Mareinkiewicz Zygmund-Kolmogorov’s and Brunk-Chung’s strong laws of large numbers are derivedin the setting of D 0, 1 -space under the condition （A’）. The D 0, 1 space version of Rohatgi’s Theorem on convergence of weighted sums is obtained.