Before revision:  These risk measures are defined on a special space of financial positions, which is called the variable exponent Bochner-Lebesgue space. This space is denoted by L^{p(\cdot)} where the variable exponent p(\cdot) is no longer a given real number like the space L^{p}, but a random variable, which reflects the possible volatility of the financial markets .
After revision:  These risk measures are defined on a special space L^{p(\cdot)} where the variable exponent p(\cdot) is no longer a given real number like the space L^{p}, but a random variable, which reflects the possible volatility of the financial markets .