that, Brezis-Véron in [@BV] found that the problem (\[local\]) admits only the zero solution if $q\geq  N/(N-2)$. Much advances in the study of semilinear second order elliptic equations involving measures see references [@BLOP; @BMP1; @MP; @P].

During the last years, there has also been a renewed and increasing interest in the study of linear and nonlinear integro-differential operators, especially, the fractional Laplacian, motivated by various applications in physics and by important links on the theory of Lévy processes, refer to [@CS2; @CS3; @CS1; @CFQ; @CKS; @CS; @CV1; @CV2; @FQ2; @S; @S1]. In a recent work, Karisen-Petitta-Ulusoy in [@KPU] used the duality approach to study the fractional elliptic equation $$(-\Delta)^\alpha v=\mu\quad{\rm{in}}\quad {\mathbb{R}}^N,$$ where $\mu$ is a Radon measure with compact support. More recently, Chen-Véron in [@CV2] studied the semilinear fractional elliptic problem (\[eq1.1\]) when $\Omega$ is an open bounded regular set in ${\mathbb{R}}^N$ and $\nu$ is a Radon measure such that $\int_{\Omega}d^\beta d|\nu|<+\infty$ with $ \beta\in[0,\alpha]$ and $d(x)=dist(x,\partial\Omega)$. The existence and uniqueness of weak solution are obtained when the function $h$ is nondecreasing and satisfies $$\label{eq 2.10wx1}
\int_1^{+\infty}(h(s)-h(-s))s^{-1-k_{\alpha,\beta}}ds<+\infty,$$ where $$\label{eq 2.10}
k_{\alpha,\beta}=\left\{
\arraycolsep=1pt
\begin{array}{lll}
\frac{N}{N-2\alpha},\quad &{\rm if}\quad
\beta\in[0,\frac{N-2\alpha}N\alpha],\\[2mm]
\frac{N+\alpha}{N-2\alpha+\beta},\quad &{\rm if}\quad
\beta\in(\frac{N-2\alpha}N\alpha,\alpha].
\end{array}
\right.$$

Motivated by these results and in view 