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Results tagged with real-analysis
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user 129192
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
1
vote
1
answer
85
views
The distance between a collection of points and a sequence of sets
Fix $m \geq 2$, and consider a sequence of sets
$$
J_m^{(n)} = \left\{ \frac{2}{mn}+\frac{i-1}{n}\right\}_{i=1}^n.
$$
For any collection of $m-1$ points $x_1,...,x_{m-1} \in (0, 1)\cap \mathbb{Q}$, de …
- 128k
1
vote
3
answers
748
views
Determining polynomial approximations of piecewise constant functions
Let $t_1 < t_2 < \cdots <t_m$ be real, and $X = \cup_{i=1}^{m-1} (t_i, t_{i+1})$ be a union of real open intervals. Let $f:X \rightarrow \{-1, 1\}$ be any piecewise constant function of form
$$
f(x) …
- 91.8k
0
votes
1
answer
87
views
Recurrence results for an "on average" measure preserving transformation
I have a finite measure space $(X, \mathcal{S}, \mu)$, and a transformation $f:X\rightarrow X$ that "preserves measure on average". That is, for $A \in \mathcal{S}$
$$
\lim_{n\rightarrow \infty} \fra …
- 1,087