query: Is there a Lebesgue measurable subset $A \subset R$ such that for every interval $(a,b)$ we have $0 < \lambda(A\cap(a,b))< (b-a)$
positive_passages.docid: 155311
positive_passages.text: How to get a set $E$ such that $0<\mu(E\cap I)<\mu(E)$ for all interval $I$?
negative_passages.docid: 19773
negative_passages.text: Is finite additivity a property of the Lebesegue outer measure?
negative_passages.docid: 154621
negative_passages.text: A set with a finite integral of measure zero?
negative_passages.docid: 68811
negative_passages.text: If $f$ is Lebesgue integrable on $[0,2]$ and $\int_E fdx=0$ for all measurable set E such that $m(E)=\pi/2$. Prove or disprove that $f=0$ a.e.
negative_passages.docid: 131037
negative_passages.text: Is every compact subset of $\Bbb{R}$ the support of some Borel measure?
negative_passages.docid: 79974
negative_passages.text: The cardinality of Lebesgue sets
negative_passages.docid: 88418
negative_passages.text: Proof of a theorem saying that we can make a measurable function continuous by altering it by a set of arbitarily small measure
negative_passages.docid: 74720
negative_passages.text: Is every set of measure zero countable?
negative_passages.docid: 59581
negative_passages.text: A function which is continuous in one variable and measurable in other is jointly measurable
negative_passages.docid: 22558
negative_passages.text: Vitali-type set with given outer measure
negative_passages.docid: 99562
negative_passages.text: "Sum" of positive measure set contains an open interval?
negative_passages.docid: 36631
negative_passages.text: Is $[0,1] \cap \Bbb Q$ a compact subset of $\Bbb Q$?
negative_passages.docid: 58827
negative_passages.text: Absolute value of a measurable function is measurable
negative_passages.docid: 128332
negative_passages.text: Counterexample to "Measurable in each variable separately implies measurable"
negative_passages.docid: 63413
negative_passages.text: For a set of positive measure there is an interval in which its density is high, $\mu(E\cap I)> \rho \mu(I)$
negative_passages.docid: 3023
negative_passages.text: Construction of a Borel set with positive but not full measure in each interval
negative_passages.docid: 135548
negative_passages.text: Every section of a measurable set is measurable? (in the product sigma-algebra)