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Example 7.4.13(d): Measurable Functions

Show that a function f is measurable if and only if
  • the set { x: f(x) < a } is measurable for all a
  • the set { x: f(x) a } is measurable for all a
  • the set { x: f(x) > a } is measurable for all a
  • the set { x: f(x) a } is measurable for all a
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