Before revision:  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:  This space is denoted by L^{p(\cdot) (\Omega, E) } L^{p(\cdot) where the variable exponent p(\cdot) is no longer a given real number like the space L^{p}, but a measurable function .