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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 ...
Define the two measures on the real line as = [,] () = [,] for all Borel sets. Then and are equivalent, since all sets outside of [,] have and measure zero, and a set inside [,] is a -null set or a -null set exactly when it is a null set with respect to Lebesgue measure.
The first group of metric units are those that are at present defined as units within the International System of Units (SI). In its most restrictive interpretation, this is what may be meant when the term metric unit is used. The unit one (1) is the unit of a quantity of dimension one. It is the neutral element of any system of units. [2]
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.
Multiples and submultiples of metric units are related by powers of ten and their names are formed with prefixes. This relationship is compatible with the decimal system of numbers and it contributes greatly to the convenience of metric units. In the early metric system there were two base units, the metre for length and the gram for mass. The ...
The metric system is a system of measurement that standardizes a set of base units and a ... a derived unit for catalytic activity equivalent to one mole per second ...
About 500,000 metric tons of food worth $340 million is in limbo, in transit or storage, as humanitarian organizations wait for U.S. State Department approval to distribute it, said Marcia Wong, a ...
The International System of Units, internationally known by the abbreviation SI (from French Système international d'unités), is the modern form of the metric system and the world's most widely used system of measurement.