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In mathematics, and specifically in measure theory, equivalence is a notion of two measures being qualitatively similar. Specifically, the two measures agree on which events have measure zero. Specifically, the two measures agree on which events have measure zero.
Equality (mathematics) Equality operator; Equipollence (geometry) Equivalence (measure theory) Equivalence class; Equivalence of categories; Equivalence of metrics; Equivalence relation; Equivalence test; Equivalent definitions of mathematical structures; Equivalent infinitesimal; Equivalent latitude; Exponentially equivalent measures ...
Conversion of units is the conversion of the unit of measurement in which a quantity is expressed, typically through a multiplicative conversion factor that changes the unit without changing the quantity. This is also often loosely taken to include replacement of a quantity with a corresponding quantity that describes the same physical property.
Two metrics and on X are strongly or bilipschitz equivalent or uniformly equivalent if and only if there exist positive constants and such that, for every ,, (,) (,) (,).In contrast to the sufficient condition for topological equivalence listed above, strong equivalence requires that there is a single set of constants that holds for every pair of points in , rather than potentially different ...
"Mathematics [...] cannot be explained completely by a single concept such as the mathematical structure. Nevertheless, Bourbaki's structuralist approach is the best that we have." (Pudlák 2013, page 3) "Evident as the notion of mathematical structure may seem these days, it was at least not made explicit until the middle of the 20th century.
Typically, such units (or indices) take another latent variable into account, for increased measurement invariance, e.g., apparent temperature, or they are more convenient in a particular context. See also: measurement equivalence , Equivalence (measure theory) , and List of unusual units of measurement
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