{"id":{"repo_id":"greece","oai_identifier":"oai:10442/1648"},"canonical_url":"https://search.dev.ndltd.org/etd/greece/oai:10442/1648","repository":{"repo_id":"greece","name":"Greek National Archive of PhD Theses","base_url":"https://phdtheses.ekt.gr/eadd_oai/request"},"display":{"title":"ΣΠΟΥΔΗ ΣΤΑ ΙΔΙΑΖΟΝΤΑ ΜΕΤΡΑ ΠΟΥ ΠΡΟΚΥΠΤΟΥΝ ΑΠΟ ΑΠΕΙΡΟΓΙΝΟΜΕΝΑ","abstract":"IN THIS THESIS WE ESTABLISH A COMPLETE SYSTEM OF WALSH FUNCTIONS, ON A COMPACT SET E, OF A LOCALLY COMPACT NON-DISCRETE METRIZABLE GROUP, HAVING POSITIVE HAARMEASURE. WE DEAL WITH RIESZ-PRODUCT TYPE MEASURES BASED ON A RADEMACHER SYSTEMOF FUNCTIONS. WE PROVE A SUFFICIENT CONDITION FOR ONE RIESZ PRODUCT MEASURE OFTHIS TYPE TO BE EQUIVALENT TO ANOTHER. ALSO WE SHOW THAT ON ANY LOCALLY COMPACT NON DISCRETE GROUP G, THERE EXIST CONTINUOUS SINGULAR MEASURES, WITH RESPECT TO THE LEFT HAAR MEASURE, WHICH HAVE ABSOLUTELY CONTINUOUS CONVOLUTION SQUARES.FURTHERMORE, WE INTRODUCE THE NOTION OF GENERALIZED RADEMACHER- RIESZ PRODUCT MEASURE. WE STUDY THE ERGODICITY OF THESE MEASURES. NEXT, WE FIND THE HAUSDORFFDIMENSION OF THE SUPPORT OF A GENERALIZED RADEMACHER-RIESZ PRODUCT. FINALLY, WE DETERMINE THE ENTROPY OF SUCH A MEASURE.","abstract_html":"IN THIS THESIS WE ESTABLISH A COMPLETE SYSTEM OF WALSH FUNCTIONS, ON A COMPACT SET E, OF A LOCALLY COMPACT NON-DISCRETE METRIZABLE GROUP, HAVING POSITIVE HAARMEASURE. WE DEAL WITH RIESZ-PRODUCT TYPE MEASURES BASED ON A RADEMACHER SYSTEMOF FUNCTIONS. WE PROVE A SUFFICIENT CONDITION FOR ONE RIESZ PRODUCT MEASURE OFTHIS TYPE TO BE EQUIVALENT TO ANOTHER. ALSO WE SHOW THAT ON ANY LOCALLY COMPACT NON DISCRETE GROUP G, THERE EXIST CONTINUOUS SINGULAR MEASURES, WITH RESPECT TO THE LEFT HAAR MEASURE, WHICH HAVE ABSOLUTELY CONTINUOUS CONVOLUTION SQUARES.FURTHERMORE, WE INTRODUCE THE NOTION OF GENERALIZED RADEMACHER- RIESZ PRODUCT MEASURE. WE STUDY THE ERGODICITY OF THESE MEASURES. NEXT, WE FIND THE HAUSDORFFDIMENSION OF THE SUPPORT OF A GENERALIZED RADEMACHER-RIESZ PRODUCT. FINALLY, WE DETERMINE THE ENTROPY OF SUCH A MEASURE.","abstract_has_math":false,"creators":["Κουμάντος, Σταμάτιος"],"institution":"Aristotle University Of Thessaloniki (AUTH)","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1991,"date_issued":"1991","date_published":"1991","updated_at":"2026-07-24T02:25:02Z","subjects":["ΑΠΕΙΡΟΓΙΝΟΜΕΝΑ ΤΟΥ RIESZ","Διάσταση Hausdorff","Εντροπία","ΕΡΓΟΔΙΚΟΤΗΤΑ","ΜΕΤΡΑ ΣΕ ΟΜΑΔΕΣ","ΣΥΝΑΡΤΗΣΕΙΣ RADEMACHER","ΣΥΝΕΛΙΞΗ ΜΕΤΡΩΝ","CONVOLUTION MEASURE ALGEBRA","Entropy","ERGODICITY","Hausdorff dimension","MEASURES ON GROUPS","RADEMACHER FUNCTIONS","Riesz products","Φυσικές Επιστήμες","Μαθηματικά","Natural Sciences","Mathematics"],"languages":["gre"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/1648"],"render_values":[{"text":"10.12681/eadd/1648","href":"https://doi.org/10.12681/eadd/1648","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10442/hedi/1648","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Κουμάντος, Σταμάτιος"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["1991"]},{"key":"dc:publisher","label":"Institution","values":["Aristotle University Of Thessaloniki (AUTH)","Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ)"]},{"key":"dc:type","label":"Dc Type","values":["PhD Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["ΑΠΕΙΡΟΓΙΝΟΜΕΝΑ ΤΟΥ RIESZ","Διάσταση Hausdorff","Εντροπία","ΕΡΓΟΔΙΚΟΤΗΤΑ","ΜΕΤΡΑ ΣΕ ΟΜΑΔΕΣ","ΣΥΝΑΡΤΗΣΕΙΣ RADEMACHER","ΣΥΝΕΛΙΞΗ ΜΕΤΡΩΝ","CONVOLUTION MEASURE ALGEBRA","Entropy","ERGODICITY","Hausdorff dimension","MEASURES ON GROUPS","RADEMACHER FUNCTIONS","Riesz products","Φυσικές Επιστήμες","Μαθηματικά","Natural Sciences","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["gre"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/1648","http://hdl.handle.net/10442/hedi/1648"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["IN THIS THESIS WE ESTABLISH A COMPLETE SYSTEM OF WALSH FUNCTIONS, ON A COMPACT SET E, OF A LOCALLY COMPACT NON-DISCRETE METRIZABLE GROUP, HAVING POSITIVE HAARMEASURE. WE DEAL WITH RIESZ-PRODUCT TYPE MEASURES BASED ON A RADEMACHER SYSTEMOF FUNCTIONS. WE PROVE A SUFFICIENT CONDITION FOR ONE RIESZ PRODUCT MEASURE OFTHIS TYPE TO BE EQUIVALENT TO ANOTHER. ALSO WE SHOW THAT ON ANY LOCALLY COMPACT NON DISCRETE GROUP G, THERE EXIST CONTINUOUS SINGULAR MEASURES, WITH RESPECT TO THE LEFT HAAR MEASURE, WHICH HAVE ABSOLUTELY CONTINUOUS CONVOLUTION SQUARES.FURTHERMORE, WE INTRODUCE THE NOTION OF GENERALIZED RADEMACHER- RIESZ PRODUCT MEASURE. WE STUDY THE ERGODICITY OF THESE MEASURES. NEXT, WE FIND THE HAUSDORFFDIMENSION OF THE SUPPORT OF A GENERALIZED RADEMACHER-RIESZ PRODUCT. FINALLY, WE DETERMINE THE ENTROPY OF SUCH A MEASURE.","ΣΤΗΝ ΕΡΓΑΣΙΑ ΑΥΤΗ ΓΙΝΕΤΑΙ ΜΕΛΕΤΗ ΑΠΕΙΡΟΓΙΝΟΜΕΝΩΝ ΤΥΠΟΥ RIESZ, ΜΕ ΣΥΝΑΡΤΗΣΕΙΣ RADEMACHER ΠΟΥ ΟΡΙΖΟΝΤΑΙ Σ'ΕΝΑ ΣΥΜΠΑΓΕΣ ΣΥΝΟΛΟ ΜΙΑΣ ΟΠΟΙΑΣΔΗΠΟΤΕ ΤΟΠΙΚΑ ΣΥΜΠΑΓΟΥΣΜΕΤΡΙΚΗΣ ΟΜΑΔΑΣ. ΜΕΛΕΤΑΤΑΙ Η ΑΜΟΙΒΑΙΑ ΟΡΘΟΓΩΝΙΟΤΗΤΑ ΚΑΙ Η ΙΣΟΔΥΝΑΜΙΑ ΔΥΟ ΜΕΤΡΩΝ ΠΟΥ ΠΡΟΚΥΠΤΟΥΝ ΑΠΟ ΤΕΤΟΙΑ ΑΠΕΙΡΟΓΙΝΟΜΕΝΑ. ΑΠΟΔΕΙΚΝΥΕΤΑΙ ΟΤΙ ΣΕ ΚΑΘΕ ΜΗ ΔΙΑΚΡΙΤΗ ΤΟΠΙΚΑ ΣΥΜΠΑΓΗ ΟΜΑΔΑ, ΥΠΑΡΧΕΙ ΙΔΙΑΖΟΝ ΜΕΤΡΟ ΠΙΘΑΝΟΤΗΤΟΣ Μ, ΤΕΤΟΙΟ ΩΣΤΕ Η ΣΥΝΕΛΙΞΗ ΜΕ ΤΟΝ ΕΑΥΤΟ ΤΟΥ Μ*Μ, ΝΑ ΕΙΝΑΙ ΜΕΤΡΟ ΑΠΟΛΥΤΑ ΣΥΝΕΧΕΣ ΩΣ ΠΡΟΣ ΤΟ ΑΡΙΣΤΕΡΟ HAAR ΜΕΤΡΟ ΤΗΣ ΟΜΑΔΑΣ. ΟΡΙΖΕΤΑΙ ΕΠΙΣΗΣ Η ΕΝΝΟΙΑ ΤΟΥ ΓΕΝΙΚΕΥΜΕΝΟΥ RADEMACHER-RIESZ ΓΙΝΟΜΕΝΟΥ ΚΑΙ ΓΙΝΕΤΑΙ ΜΕΛΕΤΗ ΤΗΣ ΕΡΓΟΔΙΚΟΤΗΤΑΣ ΤΩΝ ΜΕΤΡΩΝ ΠΟΥ ΠΡΟΚΥΠΤΟΥΝ ΑΠΟΤΑ ΑΠΕΙΡΟΓΙΝΟΜΕΝΑ ΑΥΤΑ. ΕΠΙΠΛΕΟΝ, ΠΡΟΣΔΙΟΡΙΖΕΤΑΙ Η ΕΝΤΡΟΠΙΑ ΤΩΝ ΜΕΤΡΩΝ ΑΥΤΩΝ, ΜΕ ΤΟΝ ΥΠΟΛΟΓΙΣΜΟ ΤΗΣ ΔΙΑΣΤΑΣΗΣ HAUSDORFF ΤΟΥ ΦΟΡΕΑ ΤΟΥΣ."]},{"key":"dc:title","label":"Title","values":["ΣΠΟΥΔΗ ΣΤΑ ΙΔΙΑΖΟΝΤΑ ΜΕΤΡΑ ΠΟΥ ΠΡΟΚΥΠΤΟΥΝ ΑΠΟ ΑΠΕΙΡΟΓΙΝΟΜΕΝΑ"]}]}],"canonical_facts":{"dc:creator":["Κουμάντος, Σταμάτιος"],"dc:date":["1991"],"dc:description":["IN THIS THESIS WE ESTABLISH A COMPLETE SYSTEM OF WALSH FUNCTIONS, ON A COMPACT SET E, OF A LOCALLY COMPACT NON-DISCRETE METRIZABLE GROUP, HAVING POSITIVE HAARMEASURE. WE DEAL WITH RIESZ-PRODUCT TYPE MEASURES BASED ON A RADEMACHER SYSTEMOF FUNCTIONS. WE PROVE A SUFFICIENT CONDITION FOR ONE RIESZ PRODUCT MEASURE OFTHIS TYPE TO BE EQUIVALENT TO ANOTHER. ALSO WE SHOW THAT ON ANY LOCALLY COMPACT NON DISCRETE GROUP G, THERE EXIST CONTINUOUS SINGULAR MEASURES, WITH RESPECT TO THE LEFT HAAR MEASURE, WHICH HAVE ABSOLUTELY CONTINUOUS CONVOLUTION SQUARES.FURTHERMORE, WE INTRODUCE THE NOTION OF GENERALIZED RADEMACHER- RIESZ PRODUCT MEASURE. WE STUDY THE ERGODICITY OF THESE MEASURES. NEXT, WE FIND THE HAUSDORFFDIMENSION OF THE SUPPORT OF A GENERALIZED RADEMACHER-RIESZ PRODUCT. FINALLY, WE DETERMINE THE ENTROPY OF SUCH A MEASURE.","ΣΤΗΝ ΕΡΓΑΣΙΑ ΑΥΤΗ ΓΙΝΕΤΑΙ ΜΕΛΕΤΗ ΑΠΕΙΡΟΓΙΝΟΜΕΝΩΝ ΤΥΠΟΥ RIESZ, ΜΕ ΣΥΝΑΡΤΗΣΕΙΣ RADEMACHER ΠΟΥ ΟΡΙΖΟΝΤΑΙ Σ'ΕΝΑ ΣΥΜΠΑΓΕΣ ΣΥΝΟΛΟ ΜΙΑΣ ΟΠΟΙΑΣΔΗΠΟΤΕ ΤΟΠΙΚΑ ΣΥΜΠΑΓΟΥΣΜΕΤΡΙΚΗΣ ΟΜΑΔΑΣ. ΜΕΛΕΤΑΤΑΙ Η ΑΜΟΙΒΑΙΑ ΟΡΘΟΓΩΝΙΟΤΗΤΑ ΚΑΙ Η ΙΣΟΔΥΝΑΜΙΑ ΔΥΟ ΜΕΤΡΩΝ ΠΟΥ ΠΡΟΚΥΠΤΟΥΝ ΑΠΟ ΤΕΤΟΙΑ ΑΠΕΙΡΟΓΙΝΟΜΕΝΑ. ΑΠΟΔΕΙΚΝΥΕΤΑΙ ΟΤΙ ΣΕ ΚΑΘΕ ΜΗ ΔΙΑΚΡΙΤΗ ΤΟΠΙΚΑ ΣΥΜΠΑΓΗ ΟΜΑΔΑ, ΥΠΑΡΧΕΙ ΙΔΙΑΖΟΝ ΜΕΤΡΟ ΠΙΘΑΝΟΤΗΤΟΣ Μ, ΤΕΤΟΙΟ ΩΣΤΕ Η ΣΥΝΕΛΙΞΗ ΜΕ ΤΟΝ ΕΑΥΤΟ ΤΟΥ Μ*Μ, ΝΑ ΕΙΝΑΙ ΜΕΤΡΟ ΑΠΟΛΥΤΑ ΣΥΝΕΧΕΣ ΩΣ ΠΡΟΣ ΤΟ ΑΡΙΣΤΕΡΟ HAAR ΜΕΤΡΟ ΤΗΣ ΟΜΑΔΑΣ. ΟΡΙΖΕΤΑΙ ΕΠΙΣΗΣ Η ΕΝΝΟΙΑ ΤΟΥ ΓΕΝΙΚΕΥΜΕΝΟΥ RADEMACHER-RIESZ ΓΙΝΟΜΕΝΟΥ ΚΑΙ ΓΙΝΕΤΑΙ ΜΕΛΕΤΗ ΤΗΣ ΕΡΓΟΔΙΚΟΤΗΤΑΣ ΤΩΝ ΜΕΤΡΩΝ ΠΟΥ ΠΡΟΚΥΠΤΟΥΝ ΑΠΟΤΑ ΑΠΕΙΡΟΓΙΝΟΜΕΝΑ ΑΥΤΑ. ΕΠΙΠΛΕΟΝ, ΠΡΟΣΔΙΟΡΙΖΕΤΑΙ Η ΕΝΤΡΟΠΙΑ ΤΩΝ ΜΕΤΡΩΝ ΑΥΤΩΝ, ΜΕ ΤΟΝ ΥΠΟΛΟΓΙΣΜΟ ΤΗΣ ΔΙΑΣΤΑΣΗΣ HAUSDORFF ΤΟΥ ΦΟΡΕΑ ΤΟΥΣ."],"dc:identifier":["10.12681/eadd/1648","http://hdl.handle.net/10442/hedi/1648"],"dc:language":["gre"],"dc:publisher":["Aristotle University Of Thessaloniki (AUTH)","Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ)"],"dc:subject":["ΑΠΕΙΡΟΓΙΝΟΜΕΝΑ ΤΟΥ RIESZ","Διάσταση Hausdorff","Εντροπία","ΕΡΓΟΔΙΚΟΤΗΤΑ","ΜΕΤΡΑ ΣΕ ΟΜΑΔΕΣ","ΣΥΝΑΡΤΗΣΕΙΣ RADEMACHER","ΣΥΝΕΛΙΞΗ ΜΕΤΡΩΝ","CONVOLUTION MEASURE ALGEBRA","Entropy","ERGODICITY","Hausdorff dimension","MEASURES ON GROUPS","RADEMACHER FUNCTIONS","Riesz products","Φυσικές Επιστήμες","Μαθηματικά","Natural Sciences","Mathematics"],"dc:title":["ΣΠΟΥΔΗ ΣΤΑ ΙΔΙΑΖΟΝΤΑ ΜΕΤΡΑ ΠΟΥ ΠΡΟΚΥΠΤΟΥΝ ΑΠΟ ΑΠΕΙΡΟΓΙΝΟΜΕΝΑ"],"dc:type":["PhD Thesis"]},"updated_at":"2026-07-24T02:25:02Z"}