Completeness of Lp Spaces

This lecture explores the completeness of Lp spaces for functions defined on RN with a given measure μ. It covers the Riesz-Fischer theorem, which states conditions for the existence of a subsequence converging to a function in LP. The lecture also discusses the density of Cc (RN) in LP, the concept of Schwartz functions, and their importance in L² spaces. Regular and locally finite measures are highlighted, showing their significance in the density of function classes in L². The lecture concludes by emphasizing the dense nature of certain function classes in L² spaces.