A Borel maximal eventually different family

Eventually Different Functions and Inaccessible Cardinals

An Uncountable Family of Regular Borel measures

3 ABSTRACT. Let c > 0 be a fixed constant. Let 0 ≤ r < s be an arbitrary pair of real numbers. Let a, b be any pair of real numbers such that | b − a | ≤ c(s − r). Define C s r to be the set of continuous real-valued functions on [r, s], and define C r to be the set of continuous real-valued functions on [ r, +∞). Finally, consider the following sets of Lipschitz functions:

Products of Borel fixed ideals of maximal minors

Article history: Received 21 March 2017 Received in revised form 3 April 2017 Accepted 19 May 2017 Available online xxxx MSC: 13D15 13F50 14M12

A Proximal Point Algorithm for Finding a Common Zero of a Finite Family of Maximal Monotone Operators

In this paper, we consider a proximal point algorithm for finding a common zero of a finite family of maximal monotone operators in real Hilbert spaces. Also, we give a necessary and sufficient condition for the common zero set of finite operators to be nonempty, and by showing that in this case, this iterative sequence converges strongly to the metric projection of some point onto the set of c...

Hausdorff measures of different dimensions are not Borel isomorphic

We show that Hausdorff measures of different dimensions are not Borel isomorphic; that is, the measure spaces (R, B, H) and (R, B, H) are not isomorphic if s 6= t, s, t ∈ [0, 1], where B is the σ-algebra of Borel subsets of R and H is the d-dimensional Hausdorff measure. This answers a question of B. Weiss and D. Preiss. To prove our result, we apply a random construction and show that for ever...