Definition of Hessians for \(m-\) Convex Functions as Borel Measures

In this work, \(m-\) convex functions are defined in the class of bounded upper semi-continuous functions of real arguments and a connection is established between \(m-\) convex and well-known violent \(m-\) subharmonic functions. As a consequence, we define in the class of \(m-\) convex functions, the Hessians \(H^{k}, k=1,2,\ldots ,n-m+1,\) as Borel measures.