Stochastic Integral: Isometry Continuity

This lecture covers the concept of stochastic integrals, focusing on isometry and continuity properties. It explains the extension of simple and predictable processes to larger spaces, the Hilbert space properties, and the completion of spaces. The lecture also discusses the collection of martingales, their properties, and the isomorphism between different spaces. Emphasis is placed on the continuity of martingales and the convergence of processes in various spaces.