Simple Function: Difference between revisions
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==Definition== | ==Definition== | ||
A measurable function <math>f: X \rightarrow \mathbb{R}</math> is a simple function if <math>f(X)</math> is a finite subset of <math> \mathbb{R} </math>.<ref name="Folland">Folland, Gerald B. (1999). ''Real Analysis: Modern Techniques and Their Applications'', John Wiley and Sons, ISBN 0471317160, Second edition.</ref><ref name="Craig">Craig, Katy. ''MATH 201A Lecture 11''. UC Santa Barbara, Fall 2020.</ref> The standard representation for a simple function is given by <math> f(x) = \sum_{i=1}^n c_i 1_{E_i} </math> | A measurable function <math>f: X \rightarrow \mathbb{R}</math> is a simple function if <math>f(X)</math> is a finite subset of <math> \mathbb{R} </math>.<ref name="Folland">Folland, Gerald B. (1999). ''Real Analysis: Modern Techniques and Their Applications'', John Wiley and Sons, ISBN 0471317160, Second edition.</ref><ref name="Craig">Craig, Katy. ''MATH 201A Lecture 11''. UC Santa Barbara, Fall 2020.</ref> The standard representation for a simple function is given by <math> f(x) = \sum_{i=1}^n c_i 1_{E_i} (x) </math>. | ||
==Properties of Simple Functions== | ==Properties of Simple Functions== | ||
