Event Type:

Analysis Seminar

Date/Time:

Monday, November 23, 2015 - 12:00 to 13:00

Location:

Kidder 356

Local Speaker:

Abstract:

In a 1991 paper in the Annals of Probability, Gutmann, Kemperman, Reeds, and Shepp investigate the following question. Given measurable spaces \(S\) and \(Y_j, j \in J\), measurable maps \( \pi_j : S \to Y_j\), a finite measure \(\lambda\) on \(S\) and a measurable function \(f\), \(0 \leq f \leq 1\), on \(S\), when does there exist a measurable set \(E\) such that \(f \lambda\) and \(1_E \lambda\) have the same marginals with respect to all the \(\pi_j\)? They provide several theorems and one nice class of examples. The examples can be considered as results in tomography.