Wolfgang Filter

Since about 1915 integration theory has consisted of two separate branches: the abstract theory required by probabilists and the theory, preferred by analysts, that combines integration and topology. As long as the underlying topological space is reasonably nice (e.g., locally compact with countable basis) the abstract theory and the topological theory yield the same results, but for more compli­ cated spaces the topological theory gives stronger results than those provided by the abstract theory. The possibility of resolving this split fascinated us, and it was one of the reasons for writing this book. The unification of the abstract theory and the topological theory is achieved by using new definitions in the abstract theory. The integral in this book is de­ fined in such a way that it coincides in the case of Radon measures on Hausdorff spaces with the usual definition in the literature. As a consequence, our integral can differ in the classical case. Our integral, however, is more inclusive. It was defined in the book "C. Constantinescu and K. Weber (in collaboration with A.

Since about 1915 integration theory has consisted of two separate branches: the abstract theory required by probabilists and the theory, preferred by analysts, that combines integration and topology. As long as the underlying topological space is reasonably nice (e.g., locally compact with countable basis) the abstract theory and the topological theory yield the same results, but for more compli­ cated spaces the topological theory gives stronger results than those provided by the abstract theory. The possibility of resolving this split fascinated us, and it was one of the reasons for writing this book. The unification of the abstract theory and the topological theory is achieved by using new definitions in the abstract theory. The integral in this book is de­ fined in such a way that it coincides in the case of Radon measures on Hausdorff spaces with the usual definition in the literature. As a consequence, our integral can differ in the classical case. Our integral, however, is more inclusive. It was defined in the book "C. Constantinescu and K. Weber (in collaboration with A.

This introductory text acts as a singular resource for undergraduates learning the fundamental principles and applications of integration theory. Chapters discuss: function spaces and functionals, extension of Daniell spaces, measures of Hausdorff spaces, spaces of measures, elements of the theory of real functions on R.

Die umfassende Darstellung der Eigentums-, Besitz- und Nutzungs- verhaltnisse, der Wertentwicklung sowie vor allem des Transfers land- und forstwirtschaftlichen Bodenvermogens ist Zielsetzung dieser Arbeit. Als Ausgangspunkt wird ein der Volkswirtschaftlichen Gesamtrechnung entsprechendes, stark disaggregiertes, systematisches Erfassungsschema erstellt. Unter Heranziehung existierender Boden- statistiken, Einzeluntersuchungen und erganzender Schatzungen wird dieses Schema mit empirischen Daten gefullt. Im Ergebnis zeigen sich vielfaltige Interdependenzen zwischen den einzelnen Bodenteil- markten sowie zwischen der Bodenvermogensentwicklung und der sozialen Lage der in der Landwirtschaft tatigen Personen bzw. dem Agrar- strukturwandel."