Let S(0,1) be the *-algebra of all classes Lebesgue measurable functions on unit interval (0,1) and let a complete symmetric Δ-normed *-subalgebra S(0,1), in which simple are dense, e.g., L∞(0,1), Llog(0,1), Arens algebra Lω(0,1) equipped with their natural Δ-norms. We show that there exists no non-trivial derivation commuting dyadic translations interval. type II (or I∞) von Neumann algebra, a...

We continue the analysis of reproducing pairs of weakly measurable functions, which generalize continuous frames. More precisely, we examine the case where the defining measurable functions take their values in a partial inner product space (PIP spaces). Several examples, both discrete and continuous, are presented.

These are some brief notes on the translation from Razborov’s recently-developed notion of flag algebra ([9]) into the lexicon of functions and measures on certain abstract Cantor spaces (totally disconnected compact metric spaces). 1 The objects of interest Consider a universal first-order theory T with equality in a language L that contains only predicate symbols; assume T has infinite models...

We study sets on which measurable real-valued functions on a measurable space with negligibles are determined by their range.

We define a normal form (called the canonical image) of an arbitrary measurable function of several variables with respect to a natural group of transformations; describe a new complete system of invariants of such a function (the system of joint distributions); and relate these notions to the matrix distribution, another invariant of measurable functions found earlier, which is a random matrix...

Introduction In a series of papers culminating in [Ta84], M.Talagrand, the second author and others investigated at length the properties and structure of pointwise compact sets of measurable functions. A number of problems, interesting in themselves and important for the theory of Pettis integration, were solved subject to various special axioms. It was left unclear just how far the special ax...

Let B be the Borel σ-algebra of R, and let B be the Borel σ-algebra of [−∞,∞] = R ∪ {−∞,∞}: the elements of B are those subsets of R of the form B,B ∪ {−∞}, B ∪ {∞}, B ∪ {−∞,∞}, with B ∈ B. Let (X,A , μ) be a measure space. It is a fact that if fn is a sequence of A → B measurable functions then supn fn and infn fn are A → B measurable, and thus if fn is a sequence of A → B measurable functions...