Abstract
A Bochner integral formula \(f = \mathcal{B}-\int_Y w(y)\Phi(y) d\mu(y)\) is derived that presents a function f in terms of weights w and a parametrized family of functions Φ(y), y in Y . Comparison is made to pointwise formulations, norm inequalities relating pointwise and Bochner integrals are established, G-variation and tensor products are studied, and examples are presented.
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Kainen, P.C., Vogt, A. (2013). Bochner Integrals and Neural Networks. In: Bianchini, M., Maggini, M., Jain, L. (eds) Handbook on Neural Information Processing. Intelligent Systems Reference Library, vol 49. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36657-4_6
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DOI: https://doi.org/10.1007/978-3-642-36657-4_6
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