query: Bounded measurable function and integral with charcteristic function
positive_passages.docid: 19452
positive_passages.text: Restriction of a Lebesgue integral to a subset of a measurable set.
negative_passages.docid: 93684
negative_passages.text: Show that $\mu (E \setminus A)>0$ if $A$ is a nonmeasurable subset of $X$ and $A \subseteq E$, $E$ is measurable.
negative_passages.docid: 23765
negative_passages.text: Prove that lebesgue integrable equal lebesgue measure
negative_passages.docid: 36166
negative_passages.text: Uniform continuity on (0,1) implies boundedness
negative_passages.docid: 151936
negative_passages.text: Pointwise Convergence and Convergence in the mean of Riemann-integrable functions
negative_passages.docid: 28619
negative_passages.text: Bound on integral implies bound on function
negative_passages.docid: 123132
negative_passages.text: Counterexample for a non-measurable function?
negative_passages.docid: 53425
negative_passages.text: Prove that there exists a Borel measurable function $h: \mathbb R \to \mathbb R$ such that $g= h\circ f$.
negative_passages.docid: 74876
negative_passages.text: Limit of Integral of Difference Quotients of Measurable/Bounded $f$ Being $0$ Implies $f$ is Constant
negative_passages.docid: 9159
negative_passages.text: $L^p$-norm of a non-negative measurable function
negative_passages.docid: 54008
negative_passages.text: The equivalence between Cauchy integral and Riemann integral for bounded functions
negative_passages.docid: 122585
negative_passages.text: Show that a function almost everywhere continuous is measurable
negative_passages.docid: 87702
negative_passages.text: Where are measurable functions not locally integrable?
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: 71371
negative_passages.text: Nonnegativity of integral, integral operator
negative_passages.docid: 125190
negative_passages.text: Convergence to function that is not measurable
negative_passages.docid: 52104
negative_passages.text: A pseudometric on the space of the measurable functions is complete