defined on this

USAGE SUMMARY

The phrase "defined on this" is not complete and lacks context, making it difficult to assess its correctness in written English.
It could be used in a context where something is being specified or explained in relation to a particular subject or document. Example: "The terms and conditions are defined on this page for your reference."

✓ Grammatically correct

Science

Encyclopedias

Human-verified examples from authoritative sources

Exact Expressions

30 human-written examples

A basic theorem says that there is a suitable σ-field containing all the intervals and a unique probability defined on this σ-field for which the probability of an interval is its length.

Encyclopedia Britannica

Quantum-mechanical states correspond exactly to probability measures (suitably defined) on this lattice.

SEP

Different metrics are defined on this data structure, such as MinMax and Tanimoto [27].

Journal of Cheminformatics

Let (B t)), (tge0), be 1-dimension standard Brownian motion defined on this probability space.

Advances in Difference Equations

Let ({ {B t),t ge0} } ) be a real-valued Brownian motion defined on this probability space.

Advances in Difference Equations

The basic operations of average, minimum, and maximum are not defined on this alphabet.

EURASIP Journal on Information Security

Human-verified similar examples from authoritative sources

Similar Expressions

30 human-written examples

The distribution of the expressed transcript (the Abs Call was P) was characterized by JMP4.0 according to its expression level, and genes with high and low expression levels were defined on the basis of this result.

BMC Genomics

This relationship results in a more or less constant ratio of toxicity per unit area of use and this is defined on the label of the product.

Environmental Sciences Europe

Neutrophils were defined on the size/CD16+ gate.

Plosone

and we define on this space the norm (1.6).

Fixed Point Theory and Applications

We show that this transform, applied to appropriate distributions on K, gives all classical theta functions, and that, by defining on this space of theta functions an inner product related to the K-averaged heat kernel, the unitarity of the CST transform is still preserved.

Journal of Functional Analysis

Expert writing Tips

Best practice

When using "defined on this", ensure that "this" clearly refers to a specific, well-defined entity (e.g. "defined on this probability space"). This avoids ambiguity and makes your writing more precise.

Common error

Avoid using "defined on this" when the reference of "this" is unclear or ambiguous. Instead, explicitly state what "this" refers to, such as "defined on this dataset" or "defined on this interval".

Linguistic Context

The phrase "defined on this" primarily functions as a prepositional modifier, specifying the domain or context to which a definition applies. As Ludwig AI shows, it is commonly found in scientific and mathematical writing, indicating the scope within which a term or concept is valid.

Expression frequency: Common

Frequent in

Science

80%

Encyclopedias

10%

Formal & Business

5%

Less common in

News & Media

2%

Wiki

2%

Social Media

1%

Ludwig's WRAP-UP

The phrase "defined on this" serves as a crucial element in technical writing, particularly within scientific and mathematical contexts. As noted by Ludwig AI, its primary function is to specify the precise domain or context to which a definition applies, ensuring clarity and preventing misinterpretations. The prevalence of this phrase in academic and scientific literature underscores its formal and technical nature. When employing "defined on this", ensuring that the reference of "this" is unambiguous is key to effective communication. Understanding the subtleties of this phrase, and alternatives like "specified on this" or "based on this", enables writers to express complex ideas with greater precision.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

specified on this

Indicates something explicitly mentioned or detailed in this particular context, emphasizing precision.

described on this

Highlights the presence of a description within the given context, focusing on providing details.

based on this

Indicates that something relies on or is derived from the given context, emphasizing foundation or origin.

predicated on this

Suggests that something is affirmed or based on the statement being true, implying a logical dependency.

dependent on this

Emphasizes that something relies upon or is conditioned by the given context, highlighting reliance.

grounded in this

Indicates a firm basis or foundation in the specific context, emphasizing stability and reliability.

contingent on this

Highlights that something is conditional or dependent upon the given context, emphasizing uncertainty.

established on this

Suggests that something has been created or founded on this, emphasizing validation and formalization.

located on this

Indicates a physical placement or position within the given context, emphasizing spatial relationship.

situated on this

Similar to "located on this", suggests that something is placed or positioned within the specified context, but may imply a broader perspective.

FAQs

How is "defined on this" typically used in a sentence?

The phrase "defined on this" is usually employed to specify that a term, concept, or operation is defined or applicable within a particular scope or context. For example, "The metric is "defined on this space"" indicates that the definition of the metric applies specifically to that space.

What are some alternatives to "defined on this"?

Alternatives to "defined on this" include phrases like "specified on this", "described on this", "based on this", or "established on this", depending on the specific nuance you wish to convey.

Is there a difference between "defined on this" and "defined in this"?

While both phrases indicate that something is defined within a particular context, "defined on this" often implies that the definition is intrinsic to or operates directly upon that context. "Defined in this", on the other hand, might suggest that the definition is merely present within that context but not necessarily acting on it.

When is it appropriate to use "defined on this" over other similar phrases?

Use "defined on this" when the definition is intrinsically linked to the entity referenced by "this", meaning the definition's applicability or behavior is specific to and dependent on that entity. It's preferable when the entity provides the foundation or scope for the definition.