Let F be a class of measurable functions f :S 7→ [0,1] defined on a probability space (S,A, P ). Given a sample (X1, . . . ,Xn) of i.i.d. random variables taking values in S with common distribution P , let Pn denote the empirical measure based on (X1, . . . ,Xn). We study an empirical risk minimization problem Pnf →min, f ∈ F . Given a solution f̂n of this problem, the goal is to obtain very ge...

In this research, a theoretical study has been undertaken on the density and also on the relationship between refractive index and density for aqueous solutions. A simple linear equation is suggested to show this relationship. Also, a semi-empirical equation has been developed for estimating the constant of this linear equation. By using our suggested equations, the refractive indices of aq...