Potter, Harry Thompson (Tom)2014-04-012014-04-012014-04-01http://hdl.handle.net/10222/48588In this expository thesis we describe the Bochner integral for functions taking values in a separable Banach space, and we describe how a number of standard definitions and results in real analysis can be extended for these functions, with an emphasis on Hilbert-space-valued functions. We then present a partial vector-valued version of a classical theorem on singular integrals.enBocher IntegralSingular IntegralsMeasure and Integration theoryVector-valued analysisThesis