Simplification of the majorizing measures method, with development

We update, specify, review and develop in this article the classical majorizing measures method for investigation of the local structure of random fields, belonging to X.Fernique and M.Talagrand in order to simplify and improve the constant values. Our considerations based on the generalization of the L.Arnold and P.Imkeller generalization of classical Garsia-Rodemich-Rumsey inequality.