measurable function in

USAGE SUMMARY

The phrase "measurable function in" is correct and usable in written English.
It is typically used in mathematical contexts, particularly in discussions about functions that can be measured within a certain space or framework, such as in measure theory. Example: "A measurable function in the context of real analysis is one that maps measurable sets to measurable sets."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

18 human-written examples

Let u be a nonnegative measurable function in (Omega ) such that all its positive level sets have finite measure.

Bulletin of Mathematical Sciences

If,,,, and is a nonnegative measurable function in, then we have (2.10).

Journal of Inequalities and Applications

If is an analytic self-map of and is a nonnegative measurable function in, then (2.15).

Journal of Inequalities and Applications

If is a measurable function in such that for any and then call the homogeneous function of -degree in.

Journal of Inequalities and Applications

Suppose that p > 0(p ≠ 1), 1 p + 1 q = 1, a n ≥ 0, f(x) is a non-negative measurable function in (0, ∞), then.

Journal of Inequalities and Applications

Here we give an abstract definition of the symmetric-decreasing rearrangement of u (we refer [1] and [2] for more detailed discussions on this subject): Let u be a nonnegative measurable function in (Omega subset M).

Bulletin of Mathematical Sciences

Human-verified similar examples from authoritative sources

Similar Expressions

42 human-written examples

Let M be the space of measurable functions in Ω.

Boundary Value Problems

If are measurable functions in then for (2.18).

Journal of Inequalities and Applications

Let (lambda_{i}), (i in {1, 2,ldots,m }) be m bounded measurable functions in (Q_{T}=mathbb{R}^{2N+1}times 0,T)).

Advances in Difference Equations

Let (lambda_{1}) and (lambda_{2}) be two bounded measurable functions in (Q_{T}=mathbb{R}^{2N+1}times 0,T)).

Advances in Difference Equations

Let ({psi_{j}}_{j=1}^{infty}) be a sequence of measurable functions in ((0,T)).

Boundary Value Problems

Expert writing Tips

Best practice

When defining functions in mathematical contexts, clearly specify the space in which the function is "measurable" to avoid ambiguity. For example, "a measurable function in the Lebesgue space".

Common error

Avoid using the phrase "measurable function in" without specifying the measure space. The term 'measurable' depends on the sigma-algebra being considered; without context, the statement is incomplete.

Linguistic Context

The phrase "measurable function in" functions primarily as a descriptor, specifying a characteristic of a mathematical function. It indicates that the function respects the measure-theoretic structure of the space it is defined on. Ludwig AI indicates it's correct and usable in written English.

Expression frequency: Uncommon

Frequent in

Science

100%

Less common in

News & Media

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Formal & Business

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Social Media

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Ludwig's WRAP-UP

The phrase "measurable function in" is grammatically sound and frequently encountered in scientific and academic writing. Ludwig AI confirms its validity. Its primary function is to describe a function that adheres to specific mathematical criteria related to measure theory. When using this phrase, ensure that you clearly define the space in which the function is measurable and avoid overgeneralization by always specifying the measure space. Alternatives include "integrable function in" or rephrasing to emphasize the measurability within a context.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

function that is measurable in

Adds "that is" to make the phrase a relative clause specifying the type of function.

integrable function in

Changes "measurable" to "integrable", focusing on the function's integrability rather than measurability.

function measurable within

Reorders the phrase, emphasizing the space within which the function is measurable.

function measurable on

Substitutes "in" with "on", altering the prepositional relationship.

function with measurability in

Nominalizes "measurable" to "measurability", changing the sentence structure.

function admitting measurement in

Uses "admitting measurement" instead of "measurable", providing a more descriptive alternative.

function capable of being measured in

Expands the phrase to fully express the function's capacity for measurement.

the measurability of a function in

Focuses on the abstract property of measurability rather than the function itself.

property of a function being measurable in

Highlights measurability as a property of the function.

function assessed for measurability in

Shifts focus to the assessment of the function's measurability.

FAQs

What does "measurable function in" mean in mathematical analysis?

In mathematical analysis, a "measurable function in" a given space implies that the function's domain and range are structured in such a way that the function preserves measurability of sets. This is crucial for defining integrals and other operations.

How do I use "measurable function in" in a sentence?

You can use "measurable function in" to describe a function that respects the measure structure of a given space. For example, "Let f be a measurable function in the probability space (Ω, F, P)".

What are some properties of a "measurable function"?

Some key properties include that sums, products, and limits of "measurable functions" are also measurable, making them essential in integration and probability theory.

Is there a difference between a "continuous function" and a measurable function in real analysis?

Yes, while all "continuous functions" are measurable, not all measurable functions in real analysis are continuous. Measurability is a weaker condition than continuity, focusing on the preservation of measurability rather than smoothness.