query: Show that the measure is absolutely continuous w.r.t Lebesgue measure
positive_passages.docid: 148759
positive_passages.text: The Radon-Nikodym derivative of a measure such that $|\int f'\,d\mu|\le \|f\|_{L^2}$ for $f\in C^1$
negative_passages.docid: 83665
negative_passages.text: Prove a assertion concerning Lebesgue space
negative_passages.docid: 115219
negative_passages.text: If $E$ is Lebesgue measurable, show that there exists a closed set $F$ with $F \subset E$ and $m(E\setminus F)<\epsilon$
negative_passages.docid: 36227
negative_passages.text: Show continuity or uniform continuity of $\phi: (C([0,1];\Bbb R ),||\cdot||_\infty )\to (\Bbb R, |\cdot | )$
negative_passages.docid: 97761
negative_passages.text: Show that a proper continuous map from $X$ to locally compact $Y$ is closed
negative_passages.docid: 69716
negative_passages.text: $f_x$ is Borel measurable and $f^y$ is continuous then $f$ is Borel measurable
negative_passages.docid: 143174
negative_passages.text: property of continuous function
negative_passages.docid: 55019
negative_passages.text: Lebesgue density theorem in the line
negative_passages.docid: 84359
negative_passages.text: On Lebesgue Outer Measure of an interval
negative_passages.docid: 146707
negative_passages.text: Formally show that the set of continuous functions is not measurable
negative_passages.docid: 120599
negative_passages.text: Points of a Measure Zero Sets Covered by Intervals Infinitely Many Times
negative_passages.docid: 54499
negative_passages.text: How do I show that all continuous periodic functions are bounded and uniform continuous?
negative_passages.docid: 74355
negative_passages.text: Convergence in measure and almost everywhere
negative_passages.docid: 46834
negative_passages.text: show that a distance function is continuous
negative_passages.docid: 88602
negative_passages.text: Inner regularity of Lebesgue measurable sets
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: 76607
negative_passages.text: Show that exists a continuous function in $E$ that is not bounded