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This thesis examines measure functions. A measure function has as its domain of definition a class of sets. It also must satisfy a certain additive condition. To state a concise definition of a measure function, it is convenient to define set function and completely additive set function.

Abstract In our postmodern world of relativism, it is tempting to discount proverbs and proverbial expressions as worn-out absolutisms. However, using the works of Gisela Steineckert, this thesis demonstrates the relevance of such language in modern communication and in modern poetry in particular. As is appropriate for contemporary thought, these expressions are not always used in a straightforward manner as perhaps they were originally intended. Because proverbs are so well known, Steineckert is able to make use of the depth of associations with them to expand her content. In her writing, proverbs not only explore essential truths, but Steineckert is able to use the deep associations in her readers’ minds to play with wit and irony. Gisela Steineckert was born on May 14th, 1931 to a working class family in Berlin at a time of great political and social upheaval in Germany. Formal education and academics were not promoted in her home. Although she began writing in 1943 at the age of 12, nothing was available to the public until her first book appeared in 1976. She dedicated her life to writing and has published over 2500 poems and at least 10 books. Steineckert was only 18 years old when the German Democratic Republic was established among the ruins of the Third Reich in 1949. Given her terrible experiences as a youth in the Nazi era, Steineckert whole-heartedly identified with the socialist ideals upon which the new republic was founded. Because of her age and upbringing, Steineckert was particularly well placed to play a literary role in East German society and has been able to connect people to her own personal thoughts and experiences. She fulfilled this role in East German society during the cold war and has continued to do so since German reunification in 1989. The broad based recognition, which her poems and literary work enjoy, testifies to the fact that she speaks the language of the people and understands their thoughts and concerns. This thesis explores Steineckert’s use of proverbs and proverbial expressions in her poetic discourse of love, human nature and society. It addresses their use in regards to both platonic and romantic love, our relationships to our own bodies, as well as the societal themes of religion and politics. It demonstrates how these expressions greatly enhance the depth of meaning in Steineckert’s writing and help make her works and thoughts more accessible to a broader spectrum of society. Proverbs and proverbial expressions are clearly still relevant in modern literature.

Ορισμός αναλλοίωτου ολοκληρώματος σε τοπολογικές ομάδες, η χρησιμότητα αυτού στη θεωρία αναπαραστάσεων ομάδων και η καθοριστική συμβολή αυτής της χρησιμότητας στο θεώρημα δυϊσμού του Pontryagin. / -

Paderborn, Universiẗat, Diss., 2005.

Chemnitz, Techn. Univ., Diplomarb., 2007.

The purpose of this thesis is to examine certain questions concerning the Cantor ternary set. The second chapter deals with proving that the Cantor ternary set is equivalent to the middle thirds set of [0,1], closed, compact, and has Lebesgue measure zero. Further a proof that the Cantor ternary set is a locally compact, Hausdorff topological group is given. The third chapter is concerned with establishing the existence of a Haar integral on certain topological groups. In particular if G is a locally compact and Hausdorff topological group, then there is a non-zero translation invariant positive linear form on G. The fourth chapter deals with proving that for any Haar integral I on G there exists a unique Haar measure on G that represents I.

The definition of a groupoid is presented as well as examples of common structures from which a groupoid can be formed. Haar measure existence and uniqueness theorems for topological groups are used for the construction of Haar systems on groupoids. Some Haar systems are presented in addition to an example of a groupoid which admits no Haar system.

¡§Mura¡¨ is a local lightness variation without a clear contour on a uniform surface image, which imparts an unpleasant sensation to human vision. In this study, a Haar wavelet transform (WT) method is proposed to detect the mura of the polarizer. Because of the WT capability of multi-resolution analysis for digital images, the difference of gray level between neighbor pixels in different scale of an image can be analyzed by the WT high frequency coefficient. As a result, different size muras at different location can be segmented. Because the Haar WT cannot extract all the high frequency coefficient from an image at one time, the original image is decomposed into an main image and a subimage at the beginning. The applying the WT technique to extract all the high frequency coefficients from these two images. There exist three types of mura consisting of line mura, band mura, and area mura. Experiments were extensively conducted on different frequencies and sizes of these muras. Experimental results show that the presented approach is able to detect all the line muras, but some band and area muras. The result of this study can be extended to the future researches regarding mura properties and detection methods.

Die Diplomarbeit beschäftigt sich mit der Detektion von Gesichtern in Bildern. Ausgehend von einem Überblick über bestehende Verfahren wird ein viel versprechendes Verfahren ausgewählt, vorgestellt und basierend auf neuen Erkenntnissen weiterentwickelt. Bilddaten aus dem Universitätsarchiv werden exemplarisch für die Evaluierung des Verfahrens verwendet.