  It has been proposed that an asymmetry in the electron neutrino sector may be
generated by resonant active-sterile neutrino transformations during Big Bang
Nucleosynthesis (BBN). We calculate the change in the primordial $^4$He yield
$Y$ resulting from this asymmetry, taking into account both the time evolution
of the $\nu_e$ and $\bar\nu_e$ distribution function and the spectral
distortions in these. We calculate this change in two schemes: (1) a lepton
asymmetry directly generated by $\nu_e$ mixing with a lighter right-handed
sterile neutrino $\nu_s$; and (2) a lepton asymmetry generated by a
$\nu_\tau\leftrightarrow\nu_s$ or $\nu_\mu\leftrightarrow\nu_s$ transformation
which is subsequently partially converted to an asymmetry in the
$\nu_e\bar\nu_e$ sector by a matter-enhanced active-active neutrino
transformation. In the first scheme, we find that the percentage change in $Y$
is between -1% and 9% (with the sign depending on the sign of the asymmetry),
bounded by the Majorana mass limit $m_{\nu_e}\la 1$ eV. In the second scheme,
the maximal percentage reduction in $Y$ is 2%, if the lepton number asymmetry
in neutrinos is positive; Otherwise, the percentage increase in $Y$ is $\la 5%$
for $m^2_{\nu_\mu,\nu_\tau}-m^2_{\nu_s}\la 10^4$ eV. We conclude that the
change in the primordial $^4$He yield induced by a neutrino-mixing-generated
lepton number asymmetry can be substantial in the upward direction, but limited
in the downward direction.
