Abstract: We prove the existence theorem: there are many Micro-tangent sets of each function of some residual set of c [0,1] in the sense of Hausdorff metric and that of distribution, respectively. In other words, the typical continuous function has a rich (universal) micro-tangent set structure at many points. This generalizes the results offered by Z.Buczolich [1].

Key words: Micro-tangent set, Typical continuous function, Tangent measures, Rectifiable set, Residual set