Abstract.tex

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\begin{abstract}
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In this paper we work our way up to defining the \dref{def:main}[\emph{Lebesgue Integral}] by introducing relevant definitions from Set Theory and Measure Theory. We make comparisons between the \dref{def:main}[\emph{Lebesgue Integral}] and the \dref{def:riemann}[\emph{Riemann Integral}], noting the relative strengths and weaknesses of each. 
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I will also touch on other uses of Measures Theory, including it's use in Axiomatic Probability Theory in the definition of a \dref{def:rvariable}[\emph{Random Variable}]. I do my best to provide both intuitive explanations, as well as precise/concise definitions$\ldots$ At least that was the plan, had I started sooner.
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