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This lecture covers the concept of distribution and interpolation spaces, discussing the properties and computations related to them. The instructor presents Lemmas and Proofs to demonstrate the relationships between different functions and their behaviors in various spaces. The lecture delves into the computations involving distributions and interpolation spaces, showcasing the importance of these concepts in mathematical analysis. The discussion progresses to explore the implications of compact support functions and their integration by parts. Furthermore, the lecture highlights the significance of the Farier Transform and its applications in defining functions with specific properties.