Answered: Suppose the function f is defined on a…

Suppose 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?

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.5: Permutations And Inverses

Problem 4E: 4. Let , where is nonempty. Prove that a has left inverse if and only if for every subset of .

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Suppose 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?

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