# Micro tangent sets of continuous functions

Mathematica Bohemica (2003)

- Volume: 128, Issue: 2, page 147-167
- ISSN: 0862-7959

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topBuczolich, Zoltán. "Micro tangent sets of continuous functions." Mathematica Bohemica 128.2 (2003): 147-167. <http://eudml.org/doc/249212>.

@article{Buczolich2003,

abstract = {Motivated by the concept of tangent measures and by H. Fürstenberg’s definition of microsets of a compact set $A$ we introduce micro tangent sets and central micro tangent sets of continuous functions. It turns out that the typical continuous function has a rich (universal) micro tangent set structure at many points. The Brownian motion, on the other hand, with probability one does not have graph like, or central graph like micro tangent sets at all. Finally we show that at almost all points Takagi’s function is graph like, and Weierstrass’s nowhere differentiable function is central graph like.},

author = {Buczolich, Zoltán},

journal = {Mathematica Bohemica},

keywords = {typical continuous function; Brownian motion; Takagi’s function; Weierstrass’s function; typical continuous function; Brownian motion; Takagi function; Weierstrass function},

language = {eng},

number = {2},

pages = {147-167},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Micro tangent sets of continuous functions},

url = {http://eudml.org/doc/249212},

volume = {128},

year = {2003},

}

TY - JOUR

AU - Buczolich, Zoltán

TI - Micro tangent sets of continuous functions

JO - Mathematica Bohemica

PY - 2003

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 128

IS - 2

SP - 147

EP - 167

AB - Motivated by the concept of tangent measures and by H. Fürstenberg’s definition of microsets of a compact set $A$ we introduce micro tangent sets and central micro tangent sets of continuous functions. It turns out that the typical continuous function has a rich (universal) micro tangent set structure at many points. The Brownian motion, on the other hand, with probability one does not have graph like, or central graph like micro tangent sets at all. Finally we show that at almost all points Takagi’s function is graph like, and Weierstrass’s nowhere differentiable function is central graph like.

LA - eng

KW - typical continuous function; Brownian motion; Takagi’s function; Weierstrass’s function; typical continuous function; Brownian motion; Takagi function; Weierstrass function

UR - http://eudml.org/doc/249212

ER -

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