Question: Is it true that every function with bounded variation is Borel measurable? Is it true that every function with bounded variation is Lebesgue measurable? For

Is it true that every function with bounded variation is Borel measurable? Is it true that every function with bounded variation is Lebesgue measurable? For the answer "yes": prove it. For the answer "no": provide a particular counterexample and prove it is not Borel (or Lebesgue) measurable

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