Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add hamzabellouch/agent-skills --skill real-analysis-and-measure-theorygit clone --depth 1 https://github.com/hamzabellouch/agent-skillsWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/hamzabellouch/agent-skills/real-analysis-and-measure-theory)<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/real-analysis-and-measure-theory"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/real-analysis-and-measure-theory/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/real-analysis-and-measure-theory"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/real-analysis-and-measure-theory.svg" alt="Reviewed on agentmods" width="80" height="20"></a>What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00062 | $0.00528 |
| Opus 5.5 | $0.00025 | $0.00211 |
| Sonnet 5.5 | $0.00012 | $0.00106 |
| Haiku 4.5 | $0.00006 | $0.00053 |
Grade A, and why
real-analysis-and-measure-theory scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured today.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
What it actually says
Real Analysis & Measure Theory
Foundations
- Completeness (least upper bound property), Archimedean property, density of Q.
- Sequences: Cauchy <=> convergent in R; monotone convergence; Bolzano-Weierstrass; limsup/liminf; subsequences.
- Topology of R / metric spaces: open, closed, compact (Heine-Borel: closed and bounded in R^n), connected, complete; Baire category theorem; Banach fixed point theorem (contraction -> unique fixed point).
- Continuity: epsilon-delta, sequential, preimage of open sets; uniform continuity (continuous on compact); Arzela-Ascoli.
- Differentiation: MVT, Taylor with remainder, Darboux; pathological examples: Weierstrass nowhere-differentiable function, Cantor function.
- Series: absolute convergence, rearrangement (Riemann rearrangement theorem), Cauchy product.
- Uniform convergence: preserves continuity; interchange of limit with integral/derivative requires conditions; Weierstrass M-test; Stone-Weierstrass (polynomials dense in C[a,b]).
Integration & measure
- Riemann integrable <=> bounded and a.e. continuous; Darboux sums.
- Measure: sigma-algebra, Lebesgue outer measure, measurable sets, Vitali set (non-measurable, uses choice), Borel sets, Cantor set (measure zero but uncountable).
- Lebesgue integral: simple function approximation; Monotone Convergence, Fatou, Dominated Convergence theorems; Fubini-Tonelli; Radon-Nikodym; Lebesgue differentiation theorem.
- L^p spaces: Holder, Minkowski, completeness (Riesz-Fischer); L^2 Hilbert space; modes of convergence (a.e., in measure, L^p).
- Fourier series, Parseval, convergence (Dirichlet, Carleson), Fourier transform on L^1/L^2, Plancherel.
Proof habits
State the definition; choose epsilon-delta/epsilon-N scheme (work backward to find delta); watch quantifier order; give counterexamples when a claim lacks hypotheses.
What ships with it
1 file beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- today First seen · 26 lines · 62 tokens per session scan A 653540c08b35
real-analysis-and-measure-theory is a skill published in the GitHub repository hamzabellouch/agent-skills (8 stars, last pushed today), licensed MIT. It adds 62 tokens to every session and 528 once invoked, about $0.0002 per session on Opus 5.5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-10-17.
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