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Mathematical Foundation

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Cognitive Networked Sensing and Big Data

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Abstract

This chapter provides the necessary background to support the rest of the book. No attempt has been made to make this book really self-contained. The book will survey many recent results in the literature. We often include preliminary tools from publications. These preliminary tools may be still too difficult for many of the audience. Roughly, our prerequisite is the graduate-level course on random variables and processes.

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Notes

  1. 1.

    A map f: X↦Y between two topological spaces is called Borel (or Borel measurable) if f  − 1(A) is a Borel set for any open set A.

  2. 2.

    The precise meaning of this equivalence is the following: There is an absolute constant C such that property i implies property j with parameter \(K_{j} \leq CK_{i}\) for any two properties i,j = 1, 2, 3.

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Authors and Affiliations

  1. Tennessee Technological University, Cookeville, Tennessee, USA

    Robert Qiu

  2. Utica, NY, USA

    Michael Wicks

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Qiu, R., Wicks, M. (2014). Mathematical Foundation. In: Cognitive Networked Sensing and Big Data. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4544-9_1

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