On the variational measure generated by the indefinite Lebesgue integral (Q5936678)

The author specifies the variational measure generated by the function \(\Phi\) of the variable \(E\) by the formula \[ V_\Phi(E) \equiv \inf_\delta V(\Phi, \delta, E), \] where \(\inf\) is taken with respect to all functions \(\delta: A\to (0,\infty)\), \(A\) is a fixed interval in \(R^n\). The descriptive characteristics of the Lebesgue integral in \(R^n\) is presented in terms of the total continuity of the variational measure.