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Distortion properties of quasiconformal maps
(Turun yliopisto, 2010-05-14)
In this Licentiate thesis we investigate the absolute ratio δ, j, ˜j and hyperbolic ρ metrics and their relations with each other. Various growth estimates are given for quasiconformal mpas both in plane and space. Some ...
Hyperbolic Type Geometries in Subdomains
(Turun yliopisto, 2015-03-20)
This Licentiate thesis deals with hyperbolic type geometries in planar subdomains. It is known that hyperbolic type distance is always greater in a subdomain than in the original domain. In this work we obtain certain ...
From the beginning of set theory to Lebesgue’s measure problem
(Turun yliopisto, 2020-01-16)
Descriptive set theory has its origins in Cantor’s work on pointsets in the 1870s. Cantor’s construction of real numbers and proof of the non-denumerability of real numbers were the first results towards a new theory. ...