Graduate Program in Mathematics.Demir, Selçuk.Işık, Nilgün.Vurgun, Demet.2023-03-162023-03-162009.MATH 2009 V87https://digitalarchive.library.bogazici.edu.tr/handle/123456789/15244In this thesis, Szemerédi's theorem has been translated into the ergodic problem. For this purpose, ergodic theory and its tools has been studied. The ergodic version of the theorem is equivalent to Furstenberg Multiple Reccurence Theorem. So the structure of the ergodic systems has been analyzed. Finally, ergodic theoretical proof of the theorem has been given.30cm.Ergodic theory.vii, 52 leaves;