query: Sequence of measurable functions on finite measurable set
positive_passages.docid: 25306
positive_passages.text: A countable family of point-wise bounded functions defined on finite measurable set is actually uniformly bounded on a closed subset
negative_passages.docid: 135315
negative_passages.text: Proving whether a function on the set of real sequences is a metric
negative_passages.docid: 97841
negative_passages.text: General property regarding outer measure for a nested sequence of sets (measurable or not).
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: 125190
negative_passages.text: Convergence to function that is not measurable
negative_passages.docid: 73462
negative_passages.text: Nested sequences of balls in a Banach 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: 140445
negative_passages.text: Sequence of continuous functions whose pointwise limit is discontinuous
negative_passages.docid: 82236
negative_passages.text: Extension of the Lebesgue measurable sets
negative_passages.docid: 72050
negative_passages.text: Is Lebesgue outer measure continuous from above for sets with finite Lebesgue outer measure
negative_passages.docid: 24749
negative_passages.text: Monotone functions and Borel sets
negative_passages.docid: 128897
negative_passages.text: Bounded sequence in a metric space
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: 87216
negative_passages.text: Lebesgue non-measurable function
negative_passages.docid: 63608
negative_passages.text: Cauchy sequence in a normed space
negative_passages.docid: 96286
negative_passages.text: Proving that sum of two measurable functions is measurable.
negative_passages.docid: 6632
negative_passages.text: Sequence of differentiable functions