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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## A characterization of the invertible measures

### Tom 182 / 2007

Studia Mathematica 182 (2007), 197-203 MSC: Primary 43A10, 43A22, 47B48, 46J10. DOI: 10.4064/sm182-3-1

#### Streszczenie

Let $G$ be a locally compact abelian group and $M(G)$ its measure algebra. Two measures $\mu$ and $\lambda$ are said to be equivalent if there exists an invertible measure $\varpi$ such that $\varpi \ast \mu =\lambda$. The main result of this note is the following: A measure $\mu$ is invertible iff $|\widehat{\mu }\vert \geq \varepsilon$ on $\widehat{G}$ for some $\varepsilon >0$ and $\mu$ is equivalent to a measure $\lambda$ of the form $\lambda =a +\theta$, where $a\in L^{1}(G)$ and $\theta \in M(G)$ is an idempotent measure.

#### Autorzy

• A. ÜlgerDepartment of Mathematics
Koc University
Fener Yolu, 34450, Sariyer-Istanbul, Turkey
e-mail

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