1.Measures and category on the line. 2.Liouville numbers. 3.Lebesgue measure in r-space. 4.The property of baire. 5.Non-measurable sets. 6.The Banach-Mazur game. 7.Functions of first class. 8.The theorems of lusin and egoroff. 9.Metric and topological spaces. 10.Examaples of metric functions. 11.The theorem of alexandroff. 12.Transforming linear sets into nullsets. 13.Fubini’s theorem. 14.The banach category theorem. 15.Transitive transformations. 16.Exmaples of duality. 17.The pointcaré recurrence theorem. 18.Transitive transformations. 19.The sierpinski-Erdos duality theorem. 20.Examples of duality. 21.The extended principle of duality. 22.Category measure spaces.