Convex conjugates of integral functionals
Having a measure space \((\Omega ,{\mathcal A},R),\) \(\gamma :{\mathbf R} \rightarrow [0,\infty [\) a convex function with \(\gamma (0)=0\) and \(V\) a vector space of measurable functions, the author is interested in the \(\sigma (V^{\ast \ast },V^{\ast })\)-l.s.c. regularization of the integral convex functional \(I_{\gamma }:V\rightarrow [0,\infty ]\) defined by \(I_{\gamma }(v)=\int_{\Omega }\gamma (v(\omega)) R(d\omega),\) where \(V^{\ast }\) and \(V^{\ast \ast }\) are the algebraic dual and bidual of \( V.\) In order to do this, the author studies the algebraic biconjugate of restricted functions, the conjugate on Riesz spaces and duality in Orlicz spaces.
scientific article; zbMATH DE number 1822359