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On Measure and Other Properties of a Hamel Basis

1965
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Proceedings of the American Mathematical Society
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has established [2] several interesting measure-related properties of a Hamel basis. In particular, he established the existence of a Hamel basis which contains a nonempty perfect set (and, hence, supports a nontrivial Borel measure) and commented on the plausibility of the notion that a Hamel basis should be in some sense "thick. " Our purpose is to complement Jones' results by showing, subject to the continuum hypothesis which we assume throughout, that there exists a Hamel basis which

doi:10.2307/2033895
fatcat:y2ulwmax5rhjhdbxa6h5ean5hq