with respect to the measure

USAGE SUMMARY

The phrase "with respect to the measure" is correct and usable in written English.
It can be used when discussing a specific measurement or standard in a particular context, often in academic or technical writing. Example: "The results of the experiment were analyzed with respect to the measure of accuracy."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

By Lemma 3.7.8 in [2], for any bounded function (f x,t)), which is measurable with respect to the measure (frac{partial u}{partial x_{i}}), we have iint_{U}f x,t frac{partial u}{partial x_{i}} = int_{0}^{T}dt int_{U^{t}}f x,t frac{partial u}{partial x_{i}}, (5.2) where (U^{t}={x:(x,t in U}).

Boundary Value Problems

We shall denote by L p, γ ( R n, d μ γ ( x ) ) -spaces (the Lebesgue space with respect to the measure μ γ ), the set of all measurable functions f on R + n such that the norm ∥ f ∥ L p, γ ≡ ∥ f ∥ p, γ = ( ∫ R + n | f ( x ) | p d μ γ ( x ) ) 1 / p, 1 ≤ p < ∞, is finite.

Journal of Inequalities and Applications

Let the initial distribution and joint distribution of with respect to the measure be defined as (1.4) and (1.5), respectively.

Journal of Inequalities and Applications

Let be a Markov chains field on the generalized Bethe tree whose initial distribution and joint distribution with respect to the measure and are defined by (3.14), (3.15) and (1.4), (1.5), respectively.

Journal of Inequalities and Applications

We will show that there exist stegosystems that are not secure with respect to the measure insecurity considered so far.

Theoretical Computer Science

We define a notion of measure-theoretic asymptotic degree off|Λ:Λ→Λ, with respect to the measure μϕ on the fractal set Λ.

Journal of Functional Analysis

From this and a logarithmic Sobolev inequality we easily deduce qnq∥Fr∥q ⩽ pnp∥Fr∥p for all 0 < p ⩽ q < t8 where the Lp norms are taken with respect to the measure dμh above.

Journal of Functional Analysis

In this paper we shall prove that any semicontinuous affine real function, defined on a compact convex set, satisfies the boundary barycentric calculus, with respect to the measure induced on the extremal boundary of the set by any maximal Radon probability measure.

Journal of Functional Analysis

With respect to the measure topology, (L_{0}(mathcal{M})) is a complete topological ∗-algebra.

Journal of Inequalities and Applications

where is the natural logarithmic, is expectation with respect to the measure.

Journal of Inequalities and Applications

Let (f cdot)) be a function integrable with respect to the measure (mu(cdot)).

Advances in Difference Equations

Expert writing Tips

Best practice

When using "with respect to the measure" in scientific writing, clearly define the measure being referenced to avoid ambiguity. For example, specify the statistical measure (e.g., mean, median, standard deviation) or the unit of measurement (e.g., meters, kilograms).

Common error

Avoid using "with respect to the measure" without specifying what the measure actually is. Saying "the data was analyzed with respect to the measure" is vague. Instead, clarify: "The data was analyzed with respect to the measure of central tendency, specifically the mean."

Linguistic Context

The phrase "with respect to the measure" functions as a prepositional phrase that modifies a verb or noun, specifying the criteria or standard by which something is being evaluated or considered. As Ludwig AI confirms, this phrase is grammatically sound and commonly used, particularly in technical and academic contexts.

Expression frequency: Very common

Frequent in

Science

89%

Formal & Business

5%

Encyclopedias

2%

Less common in

News & Media

1%

Reference

1%

Wiki

1%

Ludwig's WRAP-UP

In summary, "with respect to the measure" is a prepositional phrase that is used to specify the standard or criterion by which something is being evaluated. According to Ludwig AI, the phrase is grammatically correct and frequently used in scientific and academic writing. It is important to clearly define the measure being referenced to avoid ambiguity. While there are many alternatives, such as "in relation to the measure" or "regarding the measure", the key is to ensure that the chosen phrase maintains the same level of precision and clarity. The phrase's prevalence in scientific literature underscores its importance in technical communication.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

in relation to the measure

Replaces "with respect to" with "in relation to", maintaining a similar level of formality and indicating a connection or comparison to the measure.

in terms of the measure

Substitutes "with respect to" with "in terms of", focusing on evaluating something based on the specified measure.

regarding the measure

Uses "regarding" instead of "with respect to", providing a slightly less formal way to indicate that the measure is the subject of consideration.

concerning the measure

Similar to "regarding", "concerning" offers a more direct way to state that the measure is the focus.

relative to the measure

Emphasizes the comparison or dependence on the measure as a point of reference.

in accordance with the measure

Implies that something is done or assessed following the guidelines of the measure.

based on the measure

Highlights that the measure serves as the foundation or criterion for evaluation.

pursuant to the measure

A more formal way to say that something is done according to the requirements of the measure.

under the measure

Suggests that something is being considered or evaluated within the framework defined by the measure.

by the standard of the measure

Specifically indicates that something is being judged or compared against the defined measure.

FAQs

How can I use "with respect to the measure" in a sentence?

Use "with respect to the measure" to indicate the standard or criterion used for evaluation or comparison. For example, "The accuracy of the model was evaluated "with respect to the measure" of root mean squared error."

What are some alternatives to "with respect to the measure"?

You can use alternatives like "in relation to the measure", "in terms of the measure", or "regarding the measure" depending on the context.

What does "with respect to the measure" mean?

"With respect to the measure" means considering something in relation to a particular standard, criterion, or unit of measurement. It indicates that an evaluation or comparison is being made against that specific measure.

Is there a difference between ""with respect to the measure"" and "in light of the measure"?

While both phrases suggest consideration, ""with respect to the measure"" implies a direct evaluation or comparison against a defined standard, whereas "in light of the measure" suggests a more general consideration given new information or perspective from the measure.