The distribution of real-valued Q-additive functions modulo 1

THE JOINT DISTRIBUTION OF q-ADDITIVE FUNCTIONS

q-ADDITIVE FUNCTIONS AND WELL DISTRIBUTION

The ring of real-valued functions on a frame

In this paper, we define and study the notion of the real-valued functions on a frame $L$. We show that $F(L) $, consisting of all frame homomorphisms from the power set of $mathbb{R}$ to a frame $ L$, is an $f$-ring, as a generalization of all functions from a set $X$ into $mathbb R$. Also, we show that $F(L) $ is isomorphic to a sub-$f$-ring of $mathcal{R}(L)$, the ring of real-valued continu...

Pointfree topology version of image of real-valued continuous functions

Let $ { mathcal{R}} L$ be the ring of real-valued continuous functions on a frame $L$ as the pointfree  version of $C(X)$, the ring of all real-valued continuous functions on a topological space $X$. Since $C_c(X)$ is the largest subring of $C(X)$ whose elements have countable image, this motivates us to present the pointfree  version of $C_c(X).$The main aim of this paper is to present t...

Q-valued Functions Revisited

Abstract. In this note we revisit Almgren’s theory of Q-valued functions, that are functions taking values in the space AQ(R) of unorderedQ-tuples of points in R. In particular: • we give shorter versions of Almgren’s proofs of the existence of Dir-minimizing Qvalued functions, of their Hölder regularity and of the dimension estimate of their singular set; • we propose an alternative intrinsic ...