On relatively nonatomic measures

On Relatively Nonatomic Measures

Optimal-partitioning Inequalities for Nonatomic Probability Measures

Suppose fix,... ,fin are nonatomic probability measures on the same measurable space (S, S). Then there exists a measurable partition isi}"=i of 5 such that Pi(Si) > (n + 1 M)'1 for a11 i l,...,n, where M is the total mass of V?=i ßi (tne smallest measure majorizing each m). This inequality is the best possible for the functional M, and sharpens and quantifies a well-known cake-cutting theorem ...

‎On the two-wavelet localization operators on homogeneous spaces with relatively invariant measures

In ‎the present ‎paper, ‎we ‎introduce the ‎two-wavelet ‎localization ‎operator ‎for ‎the square ‎integrable ‎representation ‎of a‎ ‎homogeneous space‎ with respect to a relatively invariant measure. ‎We show that it is a bounded linear operator. We investigate ‎some ‎properties ‎of the ‎two-wavelet ‎localization ‎operator ‎and ‎show ‎that ‎it ‎is a‎ ‎compact ‎operator ‎and is ‎contained ‎in‎ a...

On nonatomic submeasures on N. III

In our earlier paper (Arch. Math. 91 (2008), 76–85), we proved that if F is a sequence of finite nonempty subsets of N such that a certain quantity t(F ) is finite, then the associated submeasure dF on N is nonatomic. In the present note, we give two curious characterizations of the set of such F ’s. Mathematics Subject Classification (2000). 05A17, 11B05, 28A12.

The nonatomic supermodular game

Article history: Received 24 February 2012 Available online 14 October 2013 JEL classification: C72