Prove that a continuous function on (0,1) has a sequence of step functions which converge pointwise to it on [0,1]
110415
Proving a sequence of step functions converges pointwise to a function $f$.
111485
Let $f(x)$ be continuous on [$0,1$] to $f(x)=0$ for each $x\in[0,1]$
148349
Uniform convergence with two sequences of functions
88610
The set of convergence of a sequence of measurable functions is measurable
65474
Given sequence of $L-$Lipschitz functions which converges pointwise, prove uniform convergence
44647
Does pointwise convergence of continuous functions on a compact set to a continuous limit imply uniform convergence on that set?
87834
How can we show that the following sequence converges?
138294
Increasing sequence of step functions and diverging Lebesgue Integrals
6632
Sequence of differentiable functions
70646
Componentwise Convergence for sequences in $\mathbb{R^{n}}$
48500
Proof of convergence of sequences
111990
Continuous function from $(0, 1]$ onto $(0, 1)$?
126212
Proving uniform continuity on an interval
135110
Pointwise convergence of $h_n(x) = x^{1+\frac{1}{2n-1}}$
6785
Equicontinuity on a compact metric space turns pointwise to uniform convergence
130916
Proving the identity functions is continuous iff $\tau_1\supseteq\tau_2$
93637
Does this sequence converge pointwise and/or in $L^1$?