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# Real Analysis : Lebesgue Measure

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Show that the sum and product of two simple functions are simple.
Show that

[Definition of simple: A real-valued function is called simple if it is measurable and assumes only a finite number of values. If is simple and ahs the values then , where .]

This problem is from Royden's Real Analysis text for graduate students.

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#### Solution Preview

Real Analysis
Text: H.L. Royden, 3rd Edition
Chapter 3 Lebesgue Measure

Problem: Show that the sum and product of two simple functions are simple.
Show that

.

[Definition of simple: A real-valued function is called simple if it is measurable and assumes only a ...

#### Solution Summary

Lebesgue Measure and DeMorgan's Law are investigated.

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