2018-12-182018-12-181923Maria, Alfred Joseph. "Additive and bounded functions of curves." (1923) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/104609">https://hdl.handle.net/1911/104609</a>.https://hdl.handle.net/1911/104609Text includes handwritten formulasIn the present paper we apply the analysis of Vitali to functions of curves of limited variation* To determine the structure of functions of limited variation we associate with every finite function an additive function, called a discard. This discard measures, in a true manner, the quantity by which the function ceases to be absolutely continuous. We demonstrate that the property which characterizes a discard is that the discard coincide with its own discard. We prove the theorem that every function of limited variation can be decomposed into the sum of a function of point values, a continuous function and a finite or infinite number of elementary discards each multiplied by a constant. Finally use is made of the preceding results to find the structure of a function of limited variation hut having no point values.24 ppengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.ThesisRICE2244reformatted digitalThesis Math. 1923 Maria