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Answered by timur in a commentcomment. 

One could introduce sets of functionfunctions with a different modulus of continuity than $r\to r^\alpha$ that would fit in between absolutely continuous functions and Hölder continuous functions.

Answered by timur in a comment. One could introduce sets of function with a different modulus of continuity than $r\to r^\alpha$ that would fit in between absolutely continuous functions and Hölder continuous functions.

Answered by timur in a comment. 

One could introduce sets of functions with a different modulus of continuity than $r\to r^\alpha$ that would fit in between absolutely continuous functions and Hölder continuous functions.

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Answered by timur in a comment. One could introduce sets of function with a different modulus of continuity than $r\to r^\alpha$ that would fit in between absolutely continuous functions and Hölder continuous functions.

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