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Results tagged with real-analysis
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user 16537
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
2
votes
Accepted
Regarding sub-additive sequences and Fekete's lemma
Here is another "natural" example. Fix an integer $b \ge 2$ and let $s_b(n)$ denote, for each $n \in \mathbf N^+$, the sum of the $b$-digits of $n$. Then $s_b$ is subadditive: This comes, e.g., from t …
- 10.5k
2
votes
Accepted
Superadditivity of the lower density
I will reuse the same trick as in the answer to Paolo's other question to show that the answer to this is still in the negative.
Let $f$ and $g$ be two upper densities (in the sense of the OP), and l …
- 10.5k
2
votes
Subsets of $\mathbb{R}^+$ closed under addition
Has anyone described or catalogued all sets of non-negative real numbers that are closed under addition?
In recent years, there has been a lot of work on the arithmetic of Puiseux monoids, that is, …
- 10.5k
3
votes
0
answers
234
views
Reference request: Darboux properties of real-valued set functions (measures, densities, etc.)
Fix a set $S$ and let $f: \mathcal P(S) \rightharpoonup \mathbf R$ be a real-valued partial function on the power set of $S$; denote by $\mathcal D$ the domain of $f$. We say that $f$ has:
(i) the w …
- 10.5k