  A function $f$ defined on $[0, 1]^d$ is called strongly chargeable if there
is a continuous vector-field $v$ such that $f(x_1, \dots,x_d)$ equals the flux
of $v$ through the rectangle $[0, x_1] \times \cdots \times [0, x_d]$ for all
$(x_1, \dots, x_d) \in [0, 1]^d$. In other words, $f$ is the primitive of the
divergence of a continuous vector-field. We prove that the sample paths of the
Brownian sheet with $d \geq 2$ parameters are almost surely not strongly
chargeable. On the other hand, those of the fractional Brownian sheet of Hurst
parameter $(H_1, \dots, H_d)$ are shown to be almost surely strongly chargeable
whenever
  \[
  \frac{H_1 + \cdots + H_d}{d} > \frac{d - 1}{d}.
  \]
