Continuity Of Power Series Power Series Banach Fixed Point Theorem Complete Metric Spaces Maximal Orthonormal Systems Are Bases Analysis Stone--Weierstrass Lattice Version Approximation Theory Carathéodory Extension Theorem Measure Theory Linearity of the Radon-Nikodym Derivative Measure Theory Unitary Images of Orthonormal Bases Functional Analysis Continuous Embedding of Inhomogeneous Into Homogeneous Sobolev Spaces Sobolev Spaces Analysis Area