Definition
LT-1
Let (X, d) be a metric space and E ⊆ X. Let h : be a function. Define μh(E) by
where
Then h is called an (exact) dimension function (or gauge function) for E if μh(E) is finite and strictly positive. There are many conventions as to the properties that h should have: Rogers (1998), for example, requires that h should be monotonically increasing for t ≥ 0, strictly positive for t > 0, and continuous on the right for all t ≥ 0.
Read more about this topic: Dimension Function
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