  For fixed size sampling designs with high entropy it is well known that the
variance of the Horvitz-Thompson estimator can be approximated by the H\'ajek
formula. The interest of this asymptotic variance approximation is that it only
involves the first order inclusion probabilities of the statistical units. We
extend this variance formula when the variable under study is functional and we
prove, under general conditions on the regularity of the individual
trajectories and the sampling design, that we can get a uniformly convergent
estimator of the variance function of the Horvitz-Thompson estimator of the
mean function. Rates of convergence to the true variance function are given for
the rejective sampling. We deduce, under conditions on the entropy of the
sampling design, that it is possible to build confidence bands whose coverage
is asymptotically the desired one via simulation of Gaussian processes with
variance function given by the H\'ajek formula. Finally, the accuracy of the
proposed variance estimator is evaluated on samples of electricity consumption
data measured every half an hour over a period of one week.
