lebesgue-measure

Computes Lebesgue outer measure and verifies measurability using Caratheodory criterion with sympy/z3.

8|1|Updated Jan 4, 2026

Search Tags:#mathematics #calculus #measure theory #lebesgue measure #outer measure #caratheodory criterion

Ready to run

npx skills add https://github.com/scooter-lacroix/Maestro --skill lebesgue-measure

💬 Prompt for ChatGPT / Claude Chat▼

Please help me install this Agent Skill.
Skill: lebesgue-measure
Source: https://github.com/scooter-lacroix/Maestro/tree/main/maestro/skills/math/math/measure-theory/lebesgue-measure
Command: npx skills add https://github.com/scooter-lacroix/Maestro --skill lebesgue-measure

SYSTEM DOCUMENTATION & REQUIREMENTS

💡 This Skill includes scripts (resource) and references (resource) components.

What problem does it solve?

This Skill provides strategies and tools for solving problems related to Lebesgue measure in the field of measure theory.

Core Features & Use Cases

Outer Measure Calculation: Compute outer measures using set coverings.
Caratheodory Criterion Application: Verify measurability using the Caratheodory criterion.
Lebesgue Measure Properties: Understand and apply fundamental properties like translation invariance and sigma-additivity.
Regularity Theorems: Utilize inner and outer regularity for measure analysis.
Use Case: When faced with a complex set in R^n, use this skill to determine its Lebesgue measure by applying outer measure construction or checking the Caratheodory criterion.

Quick Start

Use the lebesgue-measure skill to compute the outer measure of a set using sympy.

Frequently Asked Questions about lebesgue-measure

High-intent search queries and answers about installing and using this skill.

FAQPage Schema

How do I calculate the Lebesgue outer measure of a set using sympy?▼

To calculate the Lebesgue outer measure, you can use this Skill to compute set coverings symbolically with sympy. It provides strategies for constructing outer measures and determining the measure of complex sets in R^n.

How do I verify measurability using the Caratheodory criterion?▼

You can verify measurability using the Caratheodory criterion by applying the Skill's computational tools to check if a set splits every subset additively. It uses z3 for logical proof and symbolic computation to validate the criterion.

What is the best way to apply Lebesgue measure properties like translation invariance?▼

The best way to apply Lebesgue measure properties is by using the Skill's problem-solving strategies to analyze translation invariance and sigma-additivity. It helps you understand and computationally verify these fundamental measure theory properties.

Can I use this tool to utilize inner and outer regularity theorems for measure analysis?▼

Yes, you can utilize inner and outer regularity theorems for measure analysis. The Skill provides computational tools to apply these regularity theorems, allowing you to approximate the measure of sets using compact and open subsets.

Does this Skill work for computing measures of complex sets in R^n?▼

Yes, this Skill works for computing measures of complex sets in R^n. When faced with a complex set, you can use it to determine the Lebesgue measure by applying outer measure construction or checking the Caratheodory criterion.