Let dν be the metric associated with a strictly positive submeasure ν on some boolean algebra P. If dν is bounded from above by 1, Eν = 1 − dν is a (fuzzy) similarity relation on P at least w.r.t. the Lukasiewicz t-norm, but possibly also w.r.t. numerous further t-norms. In this paper, we show that under certain assumptions on P and ν, we may associate with ν in a natural way a continuous t-nor...

We show that for any abelian topological group G and arbitrary diffused submeasure μ, every continuous action of L0(μ,G) on a compact space has a fixed point. This generalizes earlier results of Herer and Christensen, Glasner, Furstenberg and Weiss, and Farah and Solecki. This also answers a question posed by Farah and Solecki. In particular, it implies that if H is of the form L0(μ,R), then H ...

Maharam algebras are complete Boolean algebras carrying a positive continuous submeasure. They were introduced and studied by Maharam in [24] in relation to Von Neumann’s problem on the characterization of measure algebras. The question whether every Maharam algebra is a measure algebra has been the main open problem in this area for around 60 years. It was finally resolved by Talagrand [31] wh...

The study aims to create an overview of access non-reimbursable funds offered by the European Union through National Rural Development Program submeasure 17.1 In this way, analysis was made current situation compensation crop, animal and plant insurance premiums on Romanian farmers these funds. This showed that became increasingly interested in crop from (PNDR) 2014-2020, amid drought. Accordin...

We show that L0(φ, H) is extremely amenable for any diffused submeasure φ and any solvable compact group H. This extends results of Herer–Christensen and of Glasner and Furstenberg–Weiss. Proofs of these earlier results used spectral theory or concentration of measure. Our argument is based on a new Ramsey theorem proved using ideas coming from combinatorial applications of algebraic topologica...

Prikry asked if it is relatively consistent with the usual axioms of ZFC that every nontrivial ccc forcing adds either a Cohen or a random real. Both Cohen and random reals have the property that they neither contain nor are disjoint from an infinite set of integers in the ground model, i.e. they are splitting reals. In this note I show that that it is relatively consistent with ZFC that every ...

For maintenance of biodiversity, mainly in sites European importance and hight natural value areas, is important the management selected semi-natural grasslands (SNaNG). In first part paper we define SNaNG habitats 7 categories (A-G), grouping several types habitats. The were defined due to financing under Rural Development Programme (RDP). Then, provide their conditions for 2014-2020, applied ...

It is a well known problem of Von Neumann whether the countable chain condition and weak distributivity of a complete Boolean algebra imply that it carries a strictly positive probability measure. It was shown recently by Balcar–Jech–Pazák and Velickovic that it is consistent with ZFC, modulo the consistency of a supercompact cardinal, that every ccc weakly distributive complete Boolean algebra...

In 1974, Sugeno introduced the notion of fuzzy measure and integral to evaluate nonadditive or non-linear quality in systems engineering. In the same year, Dobrakov independently introduced the notion of submeasure from mathematical point of view to show that most of the theory of countably additive measures remain valid for such measures. Fuzzy measures and submeasures are both special kinds o...

Let F be an arbitrary topological vector space; we shall say that a subset S of F is quasi-convex if the set of continuous affine functionals on 5 separates the points of S. If X is a Banach space and T: X -* F is a continuous linear operator, then T is quasi-convex if T(U) is quasiconvex, where U is the unit ball of X. In the case when T is compact, T(U) is quasi-convex if and only if it is af...