query: Trying to find two functions $\varphi$ measurable and $f$ continuous such that $\varphi\circ f$ isn't measurable
positive_passages.docid: 21068
positive_passages.text: Is composition of measurable functions measurable?
negative_passages.docid: 2142
negative_passages.text: Finding a set of continuous functions with a certain property 2
negative_passages.docid: 70577
negative_passages.text: Product of two Lebesgue integrable functions not Lebesgue integrable
negative_passages.docid: 99726
negative_passages.text: Proving that a function is not a contraction
negative_passages.docid: 88240
negative_passages.text: Two functions discontinuous, but sum continuous
negative_passages.docid: 149095
negative_passages.text: $f(\mathbb{R}\setminus \mathbb{Q}) \subseteq \mathbb{Q}$ and $f(\mathbb{Q}) \subseteq \mathbb{R}\setminus \mathbb{Q}$ imply that $f$ is not continuous
negative_passages.docid: 28730
negative_passages.text: product of two uniformly continuous functions is uniformly continuous
negative_passages.docid: 92638
negative_passages.text: Approximation of measurable function by simple functions
negative_passages.docid: 66391
negative_passages.text: Show that $f(x+y)=f(x)+f(y)$ implies $f$ continuous $\Leftrightarrow$ $f$ measurable
negative_passages.docid: 50111
negative_passages.text: non-continuous function satisfies $f(x+y)=f(x)+f(y)$
negative_passages.docid: 33140
negative_passages.text: Two non-homeomorphic spaces with continuous bijective functions in both directions
negative_passages.docid: 21269
negative_passages.text: Bijective continuous function between $(0 ,\infty)$ and $\mathbb{R}$.
negative_passages.docid: 27775
negative_passages.text: Proving a function is not a contraction
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: 151707
negative_passages.text: Fatou's lemma and measurable sets
negative_passages.docid: 147546
negative_passages.text: $f: \mathbf{R} \rightarrow \mathbf{R}$ monotone increasing $\Rightarrow$ $f$ is measurable
negative_passages.docid: 145017
negative_passages.text: Example of a function $f$ which is nowhere continuous but $|f|$ should be continuous at all points