This paper investigates acceptance conditions for nite automata recognizing ω-regular languages. Their expressive power and their position w.r.t. the Borel hierarchy is also studied. The full characterization for the conditions (ninf,u), (ninf,⊆) and (ninf,=) is given. The nal section provides a partial characterization of (fin,=).

Recently, there has been a growing interest in understanding the complexity of common analytic equivalence relations between separable Banach spaces via the notion of Borel reducibility in descriptive set theory (see [Bos] [FG] [FLR] [FR1] [FR2] [Me]). In general, the notion of Borel reducibility yields a hierarchy (though not linear) among equivalence relations in terms of their relative compl...

Lester Dubins and Leonard Savage posed the question as to what extent the optimal reward function U of a gambling problem varies continuously in the gambling house Γ and utility function u. Here a distance is defined for measurable houses with a Borel state space and a bounded Borel measurable utility. A trivial example shows that the mapping Γ → U is not always continuous. However, it is lower...

In this paper, we introduce a notion of epistemic equivalence between hierarchies of conditional beliefs and hierarchies of lexicographic beliefs, thus extending the standard equivalence results of Halpern (2010) and Brandenburger et al. (2007) to an interactive setting, and we show that there is a Borel surjective function, mapping each conditional belief hierarchy to its epistemically equival...

we then write sn → s(A), where A is the A method of summability. Appropriate choices of A= [an,k] for n,k ≥ 0 give the classical methods [2]. In this paper, we present various summability analogs of the strong law of large numbers (SLLN) and their rates of convergence in an unified setting, beyond the class of random-walk methods. A convolution summability method introduced in the next section ...

Harer has shown that the mapping class group is a virtual duality groupmirroring the work of Borel-Serre on arithmetic groups in semisimple Q-groups. Just as the homology of the rational Tits building provides the dualizing module for any torsion-free arithmetic group, the homology of the curve complex is the dualizingmodule for any torsion-free, finite index subgroup of the mapping class group...

Let A = (a) be a matrix-valued Borel mapping on a domain Ω ⊂ R, let b = (b) be a vector field on Ω, and let LA,bφ = a ∂xi∂xjφ + b ∂xiφ. We study Borel measures μ on Ω that satisfy the elliptic equation L∗A,bμ = 0 in the weak sense: ∫ LA,bφdμ = 0 for all φ ∈ C∞ 0 (Ω). We prove that, under mild conditions, μ has a density. If A is locally uniformly nondegenerate, A ∈ H loc and b ∈ L p loc for som...