Some new inequalities related to Jensen and Ostrowski inequalities for general Lebesgue integral are obtained. Applications for $f$-divergence measure are provided as well.
1. S. M. Ali, S. D. Silvey, A general class of coefficients of divergence of one distribution from another, textit{J. Roy. Statist. Soc. Sec B,}textbf{28}, (1966), 131-142.