Roberta Nibbi: Topology of fractals.
Diplom thesis, Ferrara 1991.
Original title: Topologia dei frattali.
CONSTRUCTION OF FRACTALS BY SYSTEMS OF CONTRACTIONS

Introduction
The Hausdorff metric
Systems of contractions of a complete metric space
Affine contractions

TOPOLOGICAL DIMENSION

Normal and functionally normal spaces
Zero-dimensional normal spaces
Spaces with topological dimension greater than zero

INVARIANT MEASURES FOR A SYSTEM OF CONTRACTIONS

Sigma-algebras
Exterior measures
Measurable functions
The integral
The space of normalized Borel measures
A contraction in Prob(X)
The coding theorem
The support of an invariant measure

HAUSDORFF DIMENSION - REGULAR AND IRREGULAR SETS

Hausdorff measures
Vitali's covering theorem
Hausdorff dimension
Fractal dimension
Density and regularity
Regular and irregular 1-sets

THE KAKEYA PROBLEM

The Kakeya problem
Marstrand's theorem
Abram Besicovitch

MULTIPLIERS AND FEFFERMAN'S EXAMPLE

Multipliers in L^p
The example of Fefferman

FRACTALS ON THE COMPUTER

A program


REFERENCES