Suppose that F : (a, b) → ℝ is an increasing function which is not necessarily strictly increasing. Let

Definition A.18. A function q : (c, d) → (a, b) is called an inverse function for F if

The functions

are called the left- and right-continuous inverse functions.

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The following lemma explains the reason for calling q− and q+ the left- and right-continuous inverse functions of F.

Lemma A.19. A function q : (c, d) → (a, ...

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