Separable Hausdorff measurable Radon spaces

This paper is a companion paper of Leão et al. (Probab. Statist. Lett. 42 (1999) 409; Proyecciones--J. Math. 23 (2004) 15), in the sense that we carry out further studies on the properties of Radon spaces, proposed in Leão (Radon spaces, Ph.D. Thesis 1999). For instance, we study topological properties of these spaces and establish an isomorphism between probabilities spaces associated with these spaces and Lebesgue spaces. In addition, we establish a general way to construct probabilities on Radon spaces.