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I know that the difference of two non-decreasing functions is a function of bounded variation. I want to iterate this process. Is the difference of two functions of bounded variation also of bounded variation?

user107952
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    Yes, due to the triangle inequality. – Symplectic Witch Jan 17 '23 at 17:34
  • As a matter of fact, the functions of bounded variation are precisely those functions which can be written as the difference of two bounded monotonic functions. From this it also follows easily that the sum and difference of two such function is also of bounded variation. – Thomas Jan 17 '23 at 17:51
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    Are you aware of this post? The first result states that the variation is the sum of the variations. – Matija Jan 17 '23 at 17:51

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