Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Entire DC Network
Hausdorff Dimension, Loren Beth Nemeth
Hausdorff Dimension, Loren Beth Nemeth
Theses Digitization Project
The purpose of this study was to define topological dimension and Hausdorff dimension, Namely metric space theory and measure theory. It was verified that in the sets of elementary geometry, the dimensions agree, while in the case of the fractals, the Hausdorff dimension is strictly larger than the topological dimension.
From Measure To Integration, Sara Hernandez Mcloughlin
From Measure To Integration, Sara Hernandez Mcloughlin
Theses Digitization Project
The thesis studies the notions of outer measure, Lebesgue measurable sets and Lebesgue measure, in detail. After developing Lebesgue integration over the real line, the Riemann integrable functions are classified as those functions whose set of points of discontinuity has measure zero. The convergence theorems are proven and it is shown how these theorems are valid under less stringent assumptions that are required for the Riemann integral. A detailed analysis of abstract measure theory for general measure spaces is given.