Applications of Measure Theory to Statistics by Gogi Pantsulaia

Author:Gogi Pantsulaia
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

5.2 Auxiliary Notions and Facts from Functional Analysis and Measure Theory

Let V be a complete metric linear space, by which we mean a vector space (real or complex) with a complete metric for which the operations of addition and scalar multiplication are continuous. When we speak of a measure on V we always mean a nonnegative measure that is defined on the Borel sets of V and is not identically zero. We write for the translation of a set by a vector .

Definition 5.2.1

([HSY], Definition 1, p. 221) A measure is said to be transverse to a Borel set if the following two conditions hold.

(i)There exists a compact set for which .

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