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The MacLane's class  of analytic functions is the class of nonconstant analytic functions in the unit disk that have asymptotic values at a dense subset of the unit circle. In thispaper, we define a subclass ℛ of  consisting of those functions that have asymptotic values at a dense subset of the unit circle reached along rectifiable asymptotic paths. We also show that the class ℛ is a proper subclass of  by constructing a function f∈ that admits no asymptotic paths of finite length

A proper subclass of Maclane's class 𝒜