Sequence of continuous functions which converges to a continuous limit
13827
Uniform convergence for sequences of functions
157485
Integral of limit of pointwise convergent sequence of non-negative measurable functions
153854
$X_{n}$ converges in probability, $f$ is continuous, $f(X_{n})$ converges in probability
44057
Pointwise but not uniform convergence of continuous functions on $[0,1]$
113122
Prove that a continuous real function with finite limits is bounded
88610
The set of convergence of a sequence of measurable functions is measurable
11586
Sequences of Real Numbers in a closed bounded interval
158344
Uniform continuous maps that converge uniformly to a function f. What can we say about f?
92734
Existence of a sequence of continuous functions convergent pointwise to the indicator function of irrational numbers
148349
Uniform convergence with two sequences of functions
107311
Convergence of a sequence and some of its subsequences
100979
Uniform continuity of a function and cauchy sequences
141484
Convergence of a sequence by convergence of sub-subsequence
123981
Is it possible to write any bounded continuous function as a uniform limit of smooth functions
58361
Is there a continuous function such that $\int_0^{\infty} f(x)dx$ converges, yet $\lim_{x\rightarrow \infty}f(x) \ne 0$?
37389
Why is this sequence of functions not uniformly convergent?
66198
Sufficient condition for convergence of a real sequence