query: poinwise limit and limit in convergence is same if they are continuous
positive_passages.docid: 151936
positive_passages.text: Pointwise Convergence and Convergence in the mean of Riemann-integrable functions
negative_passages.docid: 41057
negative_passages.text: Does $L^p$-convergence imply pointwise convergence for $C_0^\infty$ functions?
negative_passages.docid: 107399
negative_passages.text: A sequence and convergence
negative_passages.docid: 140445
negative_passages.text: Sequence of continuous functions whose pointwise limit is discontinuous
negative_passages.docid: 131927
negative_passages.text: lim inf $|a_n|=0 \implies \sum_{k=1}^\infty a_{n_k}$ converges
negative_passages.docid: 156295
negative_passages.text: Relax Egoroff's Theorem to pointwise convergence a.e. and bounded a.e. pointwise limit
negative_passages.docid: 66198
negative_passages.text: Sufficient condition for convergence of a real sequence
negative_passages.docid: 20033
negative_passages.text: Regarding convergence in probability
negative_passages.docid: 68143
negative_passages.text: The set of convergent points of a sequence of continuous functions is Borel
negative_passages.docid: 43197
negative_passages.text: Showing that two definitions of $\limsup$ are equivalent
negative_passages.docid: 40297
negative_passages.text: Proof of uniform limit of Continuous Functions
negative_passages.docid: 96889
negative_passages.text: Convergence in Probability
negative_passages.docid: 154751
negative_passages.text: $f$ brings convergent nets to convergent nets, is it continuous?
negative_passages.docid: 72960
negative_passages.text: How to prove this limit composition theorem?
negative_passages.docid: 60024
negative_passages.text: Proof that a sequence is convergent
negative_passages.docid: 94066
negative_passages.text: Prove that: {$f_n$} converges unifromly to $f$ on $E$ as $n \rightarrow \infty$ if and only if $\lim_{n\rightarrow \infty} ||f_n-f||_u = 0$
negative_passages.docid: 2239
negative_passages.text: Showing that $\{f_n \}$ converges to $f$ is equivalent to $\lim_{n\to \infty} \int_X \frac{|f_n(x)-f(x)|}{1+|f_n(x)-f(x)|}d\mu(x)=0$