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4. Prove that for a step function g on [a, b], there is a continuous function h such that g(x) = h (r) except on a set of measure less than a given arbitrary small €.

4. Prove that for a step function g on [a, b], there is a continuous function h such that g(x) = h (r) except on a set of measure less than a given arbitrary small €.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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4. Prove that for a step function g on [a, b], there is a continuous function h such that g(x) = h (r) except on a set of measure less than a given arbitrary small €.
Transcribed Image Text:4. Prove that for a step function g on [a, b], there is a continuous function h such that g(x) = h (r) except on a set of measure less than a given arbitrary small €.
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