query: If exist a measurable function 𝑓 and a continuous function 𝑔 so that 𝑓・𝑔 is non-measurable.
positive_passages.docid: 22597
positive_passages.text: Composition of measurable function and continuous function
negative_passages.docid: 50111
negative_passages.text: non-continuous function satisfies $f(x+y)=f(x)+f(y)$
negative_passages.docid: 158122
negative_passages.text: If $f$ is measurable, then support of $f$ is measurable?
negative_passages.docid: 136011
negative_passages.text: Must $f$ be continuous?
negative_passages.docid: 41937
negative_passages.text: Can one construct a non-measurable set without Axiom of choice?
negative_passages.docid: 76607
negative_passages.text: Show that exists a continuous function in $E$ that is not bounded
negative_passages.docid: 87702
negative_passages.text: Where are measurable functions not locally integrable?
negative_passages.docid: 2142
negative_passages.text: Finding a set of continuous functions with a certain property 2
negative_passages.docid: 122585
negative_passages.text: Show that a function almost everywhere continuous is measurable
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: 63309
negative_passages.text: How to find a measurable but not integrable function or a positive integrable function?
negative_passages.docid: 41683
negative_passages.text: Pre-image of a measurable set A is always measurable?
negative_passages.docid: 136795
negative_passages.text: A non-measurable set of given outer measure
negative_passages.docid: 125190
negative_passages.text: Convergence to function that is not measurable
negative_passages.docid: 138055
negative_passages.text: If $A$ has a positive Lebesgue measure then there exist subsets which are not measurable
negative_passages.docid: 53738
negative_passages.text: Monotone functions and continuity