The energy class ${}_p$ is studied for 0 < p < 1. A characterization of certain bounded plurisubharmonic functions in terms of ${ℱ}_p$ and its pluricomplex p-energy is proved.

We study the relationship between convergence in capacities of plurisubharmonic functions and the convergence of the corresponding complex Monge-Ampère measures. We find one type of convergence of complex Monge-Ampère measures which is essentially equivalent to convergence in the capacity $C_n$ of functions. We also prove that weak convergence of complex Monge-Ampère measures is equivalent to convergence in the capacity $C_{n-1}$ of functions in some case. As applications we give certain stability theorems...

We prove that if $\left(\Omega \right)\ni u_j\to u\in \left(\Omega \right)$ in Cₙ-capacity then $limin{f}_{j\to \infty }{\left(d{d}^c{u}_j\right)}^n\ge 1_{u>-\infty }{\left(d{d}^{c}u\right)}^n$. This result is used to consider the convergence in capacity on bounded hyperconvex domains and compact Kähler manifolds.

We study restrictions of ω-plurisubharmonic functions to a smooth hypersurface S in a compact Kähler manifold X. The result obtained and the characterization of convergence in capacity due to S. Dinew and P. H. Hiep [to appear in Ann. Scuola Norm. Sup. Pisa Cl. Sci.] are used to study convergence in capacity on S.