Hausdorff measure functions

Hausdorff measure

Here, instead of taking a σ-algebra as given and then defining a measure on this σ-algebra (namely, on the measurable sets), we take an outer measure as given and then define measurable sets using this outer measure. Carathéodory’s theorem states that the collection M of ν-measurable sets is a σ-algebra and that the restriction of ν to M is a complete measure. Suppose that (X, ρ) is a metric sp...

Hausdorff Measure and Lukasiewicz Languages

The paper investigates fixed points and attractors of infinite iterated function systems in Cantor space. By means of the theory of formal languages simple examples of the non-coincidence of fixed point and attractor (closure of the fixed point) are given.

Measure Theory on Hausdorff Measures

Let y = h(x) be defined for 0 < x < oo and assume values in 0 ^ y ^ + co. Let S be any linear set of points and p an arbitrary positive number. Cover S by a countable number of open intervals h , I2, • • • of lengths xx, x2 , • • • each of which is less than p, and denote by mp(S; h) the lower bound of h(xi) + h(x2) + • • • for all such coverings of S. Then m(S; h) = limp|0mp(/S; h) is called t...

Hausdorff-analytic Functions of Matrices1

Robust Hausdorff distance measure for face recognition

Face is considered to be one of the biometrics in automatic person identification. The non-intrusive nature of face recognition makes it an attractive choice. For face recognition system to be practical, it should be robust to variations in illumination, pose and expression as humans recognize faces irrespective of all these variations. In this paper, an attempt to address these issues is made ...