In this paper we prove that a subharmonic function in ℝm of finite λ-type can be represented (within some subharmonic function) as the sum of a generalized Weierstrass canonical integral and a function of finite λ-type which tends to zero uniformly on compacts of ℝm. The known Brelot-Hadamard representation of subharmonic functions in ℝm of finite order can be obtained as a corollary from this result. Moreover, some properties of R-remainders of λ-admissible mass distributions are investigated.

We consider a quasilinear elliptic problem whose left-hand side is a Leray-Lions operator of $p$-Laplacian type. If $p<\gamma <N$ and the right-hand side is a Radon measure with singularity of order $\gamma$ at $x_0\in \Omega$, then any supersolution in $W_{\mathrm{l}oc}^{1,p}\left(\Omega \right)$ has singularity of order at least $\frac{(\gamma -p)}{(p-1)}$ at $x_0$. In the proof we exploit a pointwise estimate of $𝒜$-superharmonic solutions, due to Kilpeläinen and Malý, which involves Wolff’s potential of Radon’s measure.