In this paper we prove an existence and uniqueness result for the double phase Dirichlet problem when lowest exponent is equal to 1. Our solution a function of bounded variation that simultaneously lies in suitable weighted Sobolev space found as limit sequence solutions intermediate problems whose $p$ goes As that, our approach involves study some relevant properties generalized Orlicz-Sobolev...

In this paper we study the almost universal convergence of weighted sums for sequence {x ,n } of negatively dependent (ND) uniformly bounded random variables, where a, k21 is an may of nonnegative real numbers such that 0(k ) for every ?> 0 and E|x | F | =0 , F = ?(X ,…, X ) for every n>l.