-3
votes
0answers
34 views

Approximation of non-Lipschitz (but continuous) functions by Lipschitz functions [closed]

Is there any algorithm to approximate non-Lipschitz (but continuous) functions by Lipschitz functions ?
0
votes
0answers
16 views

Show that uniform continuity implies stochastic equicontinuity

Let $\Theta$ be a metric space and assume it is compact. Let $W_t: \Omega \rightarrow \mathbb{R}^k$ be a random variable for $t\leq T$. Let $m(.,\theta): \mathbb{R}^k\rightarrow\mathbb{R}^s$. Let ...
2
votes
1answer
126 views

Find a continuous function with a prescribed continuity set

It's known that for a function $f:\mathbb{R} \rightarrow \mathbb{R}$ the set of points of discontinuity must be an $F_{\sigma}$. In the book "Understanding Analysis" by Abbott is stated in page 128 ...
0
votes
0answers
178 views

Continuity of a function

Let $f\in L^2(\mathbb{R}^3)$ with compact suppport and $z\in\mathbb{C}$. Is the following function continuous for $z\in Q = \{ z : \Re z\in [a,b], \Im \sqrt{z} \in (0,1] \}$: $$ ...