set function: meaning, definition, pronunciation and examples
C1+Academic / Technical / Mathematical
Quick answer
What does “set function” mean?
A function in mathematics that assigns a value to each set in a given collection, typically a measure or a probability.
Audio
Pronunciation
Definition
Meaning and Definition
A function in mathematics that assigns a value to each set in a given collection, typically a measure or a probability.
A function whose domain is a family of sets, often used to quantify properties like size, length, area, or probability.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage in academic mathematics. Spelling of related terms follows regional conventions (e.g., 'measure' vs. 'measure').
Connotations
Highly technical in both varieties; carries the same formal, precise connotations.
Frequency
Used exclusively in technical, mathematical contexts with equal frequency.
Grammar
How to Use “set function” in a Sentence
A set function defined on a σ-algebra.A probability measure is a special kind of set function.Vocabulary
Collocations
Usage
Meaning in Context
Business
Extremely rare or never used.
Academic
Primary context. Used in lectures, textbooks, and papers in mathematics, statistics, and theoretical computer science.
Everyday
Not used.
Technical
Core term in measure theory, probability theory, and mathematical analysis.
Vocabulary
Synonyms of “set function”
Strong
Neutral
Weak
Vocabulary
Antonyms of “set function”
Watch out
Common Mistakes When Using “set function”
- Using 'set function' to mean a function that 'sets' or configures something in programming (though informal usage exists).
- Confusing a 'set function' (domain is a family of sets) with a 'function' whose co-domain is a set.
FAQ
Frequently Asked Questions
No. A standard 'function' typically maps numbers to numbers (a point function). A 'set function' maps *sets* (collections) to numbers.
Primarily in university-level mathematics courses such as Real Analysis, Measure Theory, and Probability Theory.
Yes, some set functions (like signed measures) can take on negative values, but common examples like measures and probabilities are non-negative.
The counting measure, which assigns to each finite set the number of its elements, is a simple, intuitive set function.
Set function is usually academic / technical / mathematical in register.
Set function: in British English it is pronounced /ˈsɛt ˈfʌŋk.ʃən/, and in American English it is pronounced /ˈsɛt ˈfʌŋk.ʃən/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Think of a 'set function' as a ruler for sets—it doesn't measure points (like a point function does), but entire collections or groups of points, giving them a 'size' or 'value'.
Conceptual Metaphor
A set function is a measuring cup for abstract collections.
Practice
Quiz
What is the domain of a set function in measure theory?