Before revision:  In this paper, we study the dual representation of quasiconvex risk measures defined on a special space of financial positions, which is called the variable exponent Bochner-Lebesgue space and was studied in detail by Cheng and Xu (2013). This space is denoted by L^{p(\cdot) (\Omega, E) }  where the variable exponent p(\cdot) is no longer a given real number like the space L^{p}, but a measurable function .
After revision:  In this paper, we study the dual representation of quasiconvex risk measures defined on a special space (\Omega, E) } where the variable exponent p(\cdot) is no longer a given real number like the space L^{p}, but a measurable function .