Add to ORKGThis is a note - set in the background of some historic comments - discussing the relationship between measurability and Hamel bases for R over Q. We explicitly note that such a basis must necessarily fail to be Borel measurable (or even 'analytic' in the sense of descriptive set theory). We also discuss some constructions in the literature which yield Hamel bases which even fail to be Lebesgue measurable, and discussan elementary construction of a Hamel basis which is Lebesgue measurable
In this paper we show that if $(X,\mathcal{A})$ is a measurable space and if $Y$ is a topological mo...
In the paper to the definition of measurability of set-valued functions such a a-algebra is pres...
Ulam proved that there cannot exist a probability measure on the reals for which every set is measur...
Abstract. We say that a function f: R → R is a Hamel function if f, considered as a subset of R2, is...
We prove that the Continuum Hypothesis implies that every real number in (0,1] is the Hausdorff dime...
by Arnold W. Mi l l e r (Madison, WI) and Strashimir G. Popva s s i l e v (Sofia and Auburn, AL) Abs...
summary:In this note, we prove that the countable compactness of $\lbrace 0,1\rbrace ^{{\mathbb{R}}}...
We study the consistency strength of Lebesgue measurability for $\Sigma^1_3$ sets over a weak set th...
The purpose of this paper is to discuss certain properties of Hamel bases. In particular, we reprove...
In the paper we prove that axiom CPAgameprism, which follows from the Covering Property Axiom CPA an...
In this note we will show that for every natural number n> 0 there exists an S ⊂ [0, 1] such that...
AbstractWe consider axioms asserting that Lebesgue measure on the real line may be extended to measu...
We let: ZF = the Zermelo-Fraenkel axioms of set theory without the Axiom of Choice„(AC) . ZFC = ZF ...
Abstract. We show that an infinite-dimensional complete linear spaceX has: • a dense hereditarily Ba...
In this paper we prove that in modules, MS-measurability (in the sense of Macpherson–Steinhorn) depe...
In this paper we show that if $(X,\mathcal{A})$ is a measurable space and if $Y$ is a topological mo...
In the paper to the definition of measurability of set-valued functions such a a-algebra is pres...
Ulam proved that there cannot exist a probability measure on the reals for which every set is measur...
Abstract. We say that a function f: R → R is a Hamel function if f, considered as a subset of R2, is...
We prove that the Continuum Hypothesis implies that every real number in (0,1] is the Hausdorff dime...
by Arnold W. Mi l l e r (Madison, WI) and Strashimir G. Popva s s i l e v (Sofia and Auburn, AL) Abs...
summary:In this note, we prove that the countable compactness of $\lbrace 0,1\rbrace ^{{\mathbb{R}}}...
We study the consistency strength of Lebesgue measurability for $\Sigma^1_3$ sets over a weak set th...
The purpose of this paper is to discuss certain properties of Hamel bases. In particular, we reprove...
In the paper we prove that axiom CPAgameprism, which follows from the Covering Property Axiom CPA an...
In this note we will show that for every natural number n> 0 there exists an S ⊂ [0, 1] such that...
AbstractWe consider axioms asserting that Lebesgue measure on the real line may be extended to measu...
We let: ZF = the Zermelo-Fraenkel axioms of set theory without the Axiom of Choice„(AC) . ZFC = ZF ...
Abstract. We show that an infinite-dimensional complete linear spaceX has: • a dense hereditarily Ba...
In this paper we prove that in modules, MS-measurability (in the sense of Macpherson–Steinhorn) depe...
In this paper we show that if $(X,\mathcal{A})$ is a measurable space and if $Y$ is a topological mo...
In the paper to the definition of measurability of set-valued functions such a a-algebra is pres...
Ulam proved that there cannot exist a probability measure on the reals for which every set is measur...