The role of market research information in corporate decision making

This paper aims at understanding the role of market research information in the corporate decision making process concerning marketing decisions (4Ps). Information is an asset and resource that is essential for decision-makers so that they can define the company’s short and long term goals, execute and evaluate them. The whole process can be supported by customized research and retail measurement results.marketing, research, information, decision making, strategy

Measurable circle squaring

Laczkovich proved that if bounded subsets $A$ and $B$ of $R^k$ have the same non-zero Lebesgue measure and the box dimension of the boundary of each set is less than $k$, then there is a partition of $A$ into finitely many parts that can be translated to form a partition of $B$. Here we show that it can be additionally required that each part is both Baire and Lebesgue measurable. As special cases, this gives measurable and translation-only versions of Tarski's circle squaring and Hilbert's third problem.Comment: 40 pages; Lemma 4.4 improved & more details added; accepted by Annals of Mathematic

Measurable equidecompositions for group actions with an expansion property

Given an action of a group $\Gamma$ on a measure space $\Omega$, we provide a sufficient criterion under which two sets $A, B\subseteq \Omega$ are measurably equidecomposable, i.e., $A$ can be partitioned into finitely many measurable pieces which can be rearranged using the elements of $\Gamma$ to form a partition of $B$. In particular, we prove that every bounded measurable subset of $R^n$, $n\ge 3$, with non-empty interior is measurably equidecomposable to a ball via isometries. The analogous result also holds for some other spaces, such as the sphere or the hyperbolic space of dimension $n\ge 2$.Comment: 48 pages; accepted by JEM