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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 122.29903

**Autor: ** Erdös, Pál; Kestelman, H.; Rogers, C.A.

**Title: ** An intersection property of sets with positive measure (In English)

**Source: ** Colloq. Math. 11, 75-80 (1963).

**Review: ** The main theorem of this paper runs as follows: "Let X be a compact set. Suppose the topology in X has a countable base. Let \mu be a Carathéodory outer measure on X with the properties: (a) \mu(X) = 1, (b) \mu(**{**x**}**) = 0 for each x in X, (c) Borel sets in X are \mu-measurable, (d) if E is \mu-measurable and \epsilon > 0, then there is an open set G with E \subset G and \mu(G) < \mu(E)+\epsilon. Suppose \eta > 0 and A_{r}, r in N, are \mu-measurable subsets of X with **limsup** \mu(A_{r}) \geq \eta. Then there is a Borel set S in X with \mu(S) \geq \eta, and a sequence q_{1} < q_{2} < ..., such that every point of S is a point of condensation of the set \cup_{i \geq 1} \cap_{r \geq i} A_{qr}, and every open set containing a point of S also contains a perfect subset of \cap_{i = 0} A_{q_{j+i}} for some j".

**Reviewer: ** P.Georgiou

**Classif.: ** * 28A12 Measures and their generalizations

**Index Words: ** differentiation and integration, measure theory

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