We prove Bourgain’s Return Times Theorem for a range of exponents p and q that are outside the duality range. An oscillation result is used to prove hitherto unknown almost everywhere convergence for the signed average analog of Bourgain’s averages.

In this note we provide a simpler proof of a probabilistic analysis of the set cover problem given in [6]. We also prove these results using the language of high probability instead of using convergence in probability or convergence almost everywhere, making the previous results more precise.

In the present note we investigate norm and almost everywhere convergence of the inverse continuous wavelet transform in the variable Lebesgue space. Mathematics Subject Classification (2010): Primary 42C40, Secondary 42C15, 42B08, 42A38, 46B15.

Dobrinen and Simpson [4] introduced the notions of almost everywhere domination and uniform almost everywhere domination to study recursion theoretic analogues of results in set theory concerning domination in generic extensions of transitive models of ZFC and to study regularity properties of the Lebesgue measure on 2 in reverse mathematics. In this article, we examine one of their conjectures...

When (φn) is a sequence of positive functions in L1(R) such that the convolutions φn ? f converge in L1-norm to f for all f ∈ L1(R), then these convolutions may or may not converge almost everywhere too. There is always a subsequence (φnk ) such that at least φnk ? f converges almost everywhere to f for all f ∈ Lp(R), 1 < p < ∞. A special case of this is when the functions φn are the dilations ...

Voiculescu’s asymptotic freeness result for random matrices is improved to the sense of almost everywhere convergence. The asymptotic freeness almost everywhere is first shown for standard unitary matrices based on the computation of multiple moments of their entries, and then it is shown for rather general unitarily invariant selfadjoint random matrices (in particular, standard selfadjoint Gau...

Let (X, Y), (X1, Y1), .•, (X,, Yn ) be independent identically distributed random vectors from R dxR, and let E(I Y 1 p) < oo for some p > 1 . We wish to estimate the regression function m(x) = E(Y I X = x) by mn(x), a function of x and (X1 , Y1), .•, (X,, Yn ) . For large classes of kernel estimates and nearest neighbor estimates, sufficient conditions are given for E { l m(x) m(x) 0 ) -* 0 as...

The statement of Conjecture 1.1 does not specify the convergence notion for u → u nor the solution notion for equation (1.1). We shall tacitly assume in the following that the convergence is (at least) almost everywhere in space and time, that convergence holds (at least) for subsequences, and that equation (1.1) will be solved (at least) in the distributional sense. Along with these provisions...

in this paper, we introduce a new type of almost statistical convergence of generalized difference sequences of fuzzy numbers. we give the relations between the strongly almost cesàro type convergence and almost statistical convergence in these spaces. furthermore, we study some of their properties like completeness, solidity, symmetricity etc. we also give some inclusion relations related to t...