measurable function over

USAGE SUMMARY

The phrase "measurable function over" is correct and usable in written English.
It is typically used in mathematical contexts, particularly in discussions about functions defined on measurable spaces or in measure theory. Example: "A measurable function over a given measurable space must satisfy certain properties related to the sigma-algebra."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

1 human-written examples

For and a weight, we denote the weighted -norm of a measurable function over by (1.1).

Journal of Inequalities and Applications

Human-verified similar examples from authoritative sources

Similar Expressions

59 human-written examples

The MIF method exploits the absolute continuity of admissible indemnification functions and formulates optimal reinsurance model into a functional linear programming of determining an optimal measurable function valued over a bounded interval.

Insurance: Mathematics and Economics

The integral average of a measurable function f over Q is written m_{Q}(f)= fint_{Q} f(x),dx= frac{1}{|Q|} int_{Q} f(x),dx.

Journal of Inequalities and Applications

Lebesgue measure, measurable functions, integrability, completeness of L-p spaces.

Massachusetts Institute of Technology

Let J : = [ 0, 1 ] and L 1 ( J, E ) denote the Banach space of real-valued Lebesgue integrable functions on the interval J, L ∞ ( J, E ) denote the Banach space of real-valued essentially bounded and measurable functions defined over J with the norm ∥ ⋅ ∥ L ∞.

Advances in Difference Equations

where the kernel is a nonnegative measurable function defined for and the summation is over all ordered -tuples.

Journal of Inequalities and Applications

where the kernel K ( x, y ) is a nonnegative measurable function defined for x ≠ y, and the summation is over all ordered l-tuples I.

Journal of Inequalities and Applications

Similar statements can be made about a measurable function in $\mathbb R^n$.

University of California, Berkeley

The appropriate restriction is that a random variable must be a measurable function.

Encyclopedia Britannica

where is a measurable function.

Journal of Inequalities and Applications

A function is called N- measurable on if for every measurable function the function is measurable.

Boundary Value Problems

Expert writing Tips

Best practice

When using the phrase "measurable function over", ensure that the context clearly defines the domain or set over which the function is measurable. Clarity is key in mathematical writing.

Common error

Avoid using "measurable function over" without specifying the set or space. Always provide sufficient context to prevent ambiguity.

Linguistic Context

The phrase "measurable function over" functions as a mathematical descriptor, specifying that a function satisfies the conditions of measurability within a defined space or domain. This is crucial for advanced mathematical analysis. As Ludwig suggests, it is a valid phrase.

Expression frequency: Rare

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Encyclopedias

0%

Ludwig's WRAP-UP

In summary, "measurable function over" is a technically correct phrase used primarily in mathematical and scientific contexts to describe functions that meet specific measurability criteria within a defined space. Ludwig identifies the phrase as valid, though relatively rare. When employing this phrase, ensure that the domain is clearly defined to avoid ambiguity. Alternatives like "measurable function defined on" or "measurable function on" may be used depending on the nuance you wish to convey. Remember, precision and clarity are key when discussing mathematical concepts.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

measurable function defined over

Changes the verb from "over" to "defined over" providing a more explicit description.

measurable function on

Replaces "over" with "on", offering a slightly broader scope of application.

measurable function across

Uses "across" instead of "over", suggesting a traversal or application over a range.

function measurable over

Inverts the word order, emphasizing the type of function first.

measurable function spanning

Replaces "over" with "spanning" implying that the function extends across a range.

measurable function covering

Uses "covering" instead of "over", suggesting that the function addresses all parts of a domain.

measurable function throughout

Replaces "over" with "throughout", indicating the function applies to all parts of something.

measurable function for

Substitutes "over" with "for", changing the emphasis to the purpose of the function.

measurable function considering

Uses "considering" in place of "over", suggesting the function takes into account a particular domain.

measurable function acting on

Changes to "acting on", implying that the function is performing some action on a set.

FAQs

How is "measurable function over" used in mathematical contexts?

In mathematics, "measurable function over" specifies that a function is measurable with respect to a particular sigma-algebra on a given set. This implies that the function's behavior is well-defined and can be integrated or otherwise analyzed within that specific space.

What are some alternatives to "measurable function over"?

Some alternatives include "measurable function defined on", "measurable function with respect to", or simply "measurable function on" depending on the context. Another alternative is "measurable function acting on".

What makes a function "measurable"?

A function is measurable if the preimage of every measurable set in its codomain is a measurable set in its domain. This property is crucial for integration and other analytical operations in measure theory.

Is there a difference between "measurable function on" and "measurable function over"?

While often used interchangeably, "measurable function on" typically refers to a function defined on a specific set, while "measurable function over" might imply a broader application across a range or space. The difference is subtle and context-dependent; both are valid.