DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-01

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The mollifier family generated by a unit-mass smooth bump

Definition

Let $φ \in C_{c}^{\infty} (R^{n})$ satisfy

$\int_{R^{n}} φ (x) d x = 1.$

For $ε > 0$ , define

$φ_{ε} (x) : = ε^{- n} φ (x / ε) (x \in R^{n}) .$

The family $(φ_{ε})_{ε > 0}$ is the mollifier family generated by $φ$ .

Depends on

Used by

Dependency tree · two levels

6 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Richard L. Wheeden and Antoni Zygmund, Measure and Integral: An Introduction to Real Analysis (standard reference, not scraped)
Walter Rudin, Real and Complex Analysis, 3rd ed. (standard reference, not scraped)