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 Ar, r in N, are \mu-measurable subsets of X with limsup \mu(Ar) \geq \eta. Then there is a Borel set S in X with \mu(S) \geq \eta, and a sequence q1 < q2 < ..., such that every point of S is a point of condensation of the set \cupi \geq 1 \capr \geq i Aqr, and every open set containing a point of S also contains a perfect subset of \capi = 0 Aq_{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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