This book contains details of the properties that satisfy certain function spaces and vector-valued distributions defined in the n-dimensional torus. In particular, the text deals with an introductory ...

If the space of all real-valued functions of bounded variation on a real closed interval is endowed with the topology of simple convergence, then every bounded subset which is bounded for the values ...

Let $X$ be a Banach space with dual $X^\ast$ and let $(\Omega, \Sigma, \mu)$ be a finite measure space. Suppose $f: \Omega \rightarrow X$ is weakly measurable. There ...