Suppose that the function f is defined on a measurable set E and has the property that {x ∈ E|f (x) > c} is measurable for each rational number c. Is f necessarily measurable? Prove your result. Let f be a function with measurable domain D. Show that f is measurable if and only if the function g defined on R by g(x) = f (x) for x ∈ D and g(x) = 0 for x /∈ D is measurable.

Suppose that the function f is defined on a measurable set E and has the property that {x ∈ E|f (x) > c} is measurable for each rational number c. Is f necessarily measurable? Prove your result. Let f be a function with measurable domain D. Show that f is measurable if and only if the function g defined on R by g(x) = f (x) for x ∈ D and g(x) = 0 for x /∈ D is measurable.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter6: Applications Of The Derivative

Section6.CR: Chapter 6 Review

Problem 2CR

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