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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.
Then the measure is said to be absolutely continuous in reference to if and only if . This is denoted as ν ≪ μ . {\displaystyle \nu \ll \mu .} The two measures are called equivalent if and only if μ ≪ ν {\displaystyle \mu \ll \nu } and ν ≪ μ , {\displaystyle \nu \ll \mu ,} [ 1 ] which is denoted as μ ∼ ν . {\displaystyle \mu ...
They may have apparent, effective or equivalent in their names as well. 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.
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 ...
For (,) a measurable space, a sequence μ n is said to converge setwise to a limit μ if = ()for every set .. Typical arrow notations are and .. For example, as a consequence of the Riemann–Lebesgue lemma, the sequence μ n of measures on the interval [−1, 1] given by μ n (dx) = (1 + sin(nx))dx converges setwise to Lebesgue measure, but it does not converge in total variation.
In mathematics, equivalent definitions are used in two somewhat different ways. First, within a particular mathematical theory (for example, Euclidean geometry ), a notion (for example, ellipse or minimal surface ) may have more than one definition.
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