Tailoring three-point functions and integrability IV. Θ-morphism

On Pre-θ-Open Sets and Two Classes of Functions

On Θ-precontinuous Functions

We introduce a new class of functions called θ-precontinuous functions which is contained in the class of weakly precontinuous (or almost weakly continuous) functions and contains the class of almost precontinuous functions. It is shown that the θprecontinuous image of a p-closed space is quasi H-closed. 2000 Mathematics Subject Classification. 54C08.

Integrability of Superharmonic Functions and Subharmonic Functions

We apply the coarea formula to obtain integrability of superharmonic functions and nonintegrability of subharmonic functions. The results involve the Green function. For a certain domain, say Lipschitz domain, we estimate the Green function and restate the results in terms of the distance from the boundary.

Abelian Complexity of Fixed Point of Morphism

We study the combinatorics of vtm, a variant of the Thue-Morse word generated by the non-uniform morphism 0 7→ 012, 1 7→ 02, 2 7→ 1 starting with 0. This infinite ternary sequence appears a lot in the literature and finds applications in several fields such as combinatorics on words; for example, in pattern avoidance it is often used to construct infinite words avoiding given patterns. It has b...

Integrability and τ - functions on

v Acknowledgments vi Chapter