We study the pointwise properties of $k$-subharmonic functions,
that is, the viscosity subsolutions to the fully nonlinear elliptic
equations $F_k[u]=0$, where $F_k[u]$ is the elementary symmetric
function of order $k,1\leq k\leq n$, of the eigenvalues of $[D\sp
2u]$, $F_1[u]=\Delta u,F_n[u]=\det D^2u$. Thus
$1$-subharmonic functions are subharmonic in the classical sense;
$n$-subharmonic functions are convex. We use a special capacity to
investigate the typical questions of potential theory: local
behaviour, removability of singularities, and polar, negligible, and
thin sets, and we obtain estimates for the capacity in terms of the
Hausdorff measure. We also prove the Wiener test for the regularity of
a boundary point for the Dirichlet problem for the fully nonlinear
equation $F_k[u]=0$. The crucial tool in the proofs of these
results is the Radon measure $F_k[u]$ introduced recently by
N. Trudinger and X.-J. Wang for any $k$-subharmonic $u$. We use ideas
from the potential theories both for the complex Monge-Ampère
and for the $p$-Laplace equations.