In this note we characterize cr-finite Riesz measures that allow one to approximate measurable functions by continuous functions in the sense of Lusin's theorem. We call such measures Lusin measures and show that not all cr-finite measures are Lusin measures. It is shown that if a topological space X is either normal or countably paracompact, then every measure on A' is a Lusin measure. A count...

We show that the Lusin area function and essentially all of its realvariable generalizations are pointwise dominated by an “intrinsic” square function, and that this latter function is, for all practical purposes, no larger than a “generic” square function. 0. Introduction. The Lusin area (or “square”) function is a familiar object. If f : R 7→ R is such that u(x, y) ≡ Py ∗ f(x), the Poisson in...

Assuming the continuum hypothesis there is an inseparable sequence of length ω1 that contains no Lusin subsequence, while if Martin’s Axiom and ¬CH is assumed then every inseparable sequence (of length ω1) is a union of countably many Lusin subsequences.

Assuming the continuum hypothesis there is an inseparable sequence of length ω1 that contains no Lusin subsequence, while if Martin’s Axiom and ¬CH is assumed then every inseparable sequence (of length ω1) is a union of countably many Lusin subsequences. 2000 Mathematics Subject Classification . 03E05 (Combinatorial set theory), 03E50 (Continuum hypothesis and Martin’s axiom), 03E35 ( Consisten...

Carlheinz Gräter, Jörg Lusin: Kirchen, Klöster und Kapellen in Hohenlohe. Geschichte Geschichten. Mit Fotografien von Rainer Fieselmann, Lusin Irmgard Rohloff sowie Luftaufnahmen Siegried Geyer. Stuttgart (Silberburg) 2007. 167 S.

We prove that for any semi-Dirichlet form (ε, D(ε)) on a measurable Lusin space E there exists a Lusin topology with the given σ-algebra as the Borel σ-algebra so that (ε, D(ε)) becomes quasi–regular. However one has to enlarge E by a zero set. More generally a corresponding result for arbitrary L-resolvents is proven.

Herein, we generalize and extend some standard results on the separation and convergence of probability measures. We use homeomorphism-based methods and work on incomplete metric spaces, Skorokhod spaces, Lusin spaces or general topological spaces. Our contributions are twofold: We dramatically simplify the proofs of several basic results in weak convergence theory and, concurrently, extend the...

In an !1{saturated nonstandard universe a cut is an initial segment of the hyperintegers, which is closed under addition. Keisler and Leth in [KL] introduced, for each given cut U , a corresponding U{topology on the hyperintegers by letting O be U open if for any x 2 O there is a y greater than all the elements in U such that the interval [x y; x+y] O. Let U be a cut in a hypernite time line H,...

Let X be a metric space with doubling measure, L be a nonnegative selfadjoint operator in L2(X ) satisfying the Davies-Gaffney estimate, ω be a concave function on (0,∞) of strictly lower type pω ∈ (0, 1] and ρ(t) = t/ω(t) for all t ∈ (0,∞). The authors introduce the Orlicz-Hardy space Hω,L(X ) via the Lusin area function associated to the heat semigroup, and the BMO-type space BMOρ,L(X ). The ...