query: Trying to show that a function is zero almost everywhere given a constraint on its Lebesgue measure.
positive_passages.docid: 82588
positive_passages.text: If $\int_0^x f \ dm$ is zero everywhere then $f$ is zero almost everywhere
negative_passages.docid: 44270
negative_passages.text: $E$ measurable set and $m(E\cap I)\le \frac{1}{2}m(I)$ for any open interval, prove $m(E) =0$
negative_passages.docid: 123806
negative_passages.text: How do I show that the integral of $e^{inx}$ over a set of measure $1$ is nonzero for some nonzero $n$?
negative_passages.docid: 128026
negative_passages.text: Weak derivatives equals zero
negative_passages.docid: 19452
negative_passages.text: Restriction of a Lebesgue integral to a subset of a measurable set.
negative_passages.docid: 137099
negative_passages.text: Lebesgue measure of the set of zeroes of Brownian motion
negative_passages.docid: 54137
negative_passages.text: Find a non-negative function on [0,1] such that $t\cdot m(\{x:f(x) \geq t\}) \to 0$ that is not Lebesgue Integrable
negative_passages.docid: 148555
negative_passages.text: Prove that every Lebesgue measurable function is equal almost everywhere to a Borel measurable function
negative_passages.docid: 126017
negative_passages.text: Entire function having simple zero at the Gaussian integers
negative_passages.docid: 17764
negative_passages.text: What's the relationship between Borel set and set whose boundary is measure zero?
negative_passages.docid: 90540
negative_passages.text: What is wrong in this proof: That $\mathbb{R}$ has measure zero
negative_passages.docid: 131664
negative_passages.text: Why is any Lebesgue-Stieltjes measure on $(\mathbb{R},\mathcal{B}_\mathbb{R})$ not complete?
negative_passages.docid: 76607
negative_passages.text: Show that exists a continuous function in $E$ that is not bounded
negative_passages.docid: 131444
negative_passages.text: Local maximum implies derivative is $0$
negative_passages.docid: 66951
negative_passages.text: Proving the existence of a sequence of functions converging to 0 with an added property
negative_passages.docid: 57462
negative_passages.text: Lebesgue Measure of the Graph of a Function
negative_passages.docid: 20810
negative_passages.text: Boundary of Ball of radius R has zero measure