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  2. Equivalence (measure theory) - Wikipedia

    en.wikipedia.org/wiki/Equivalence_(measure_theory)

    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.

  3. Measure (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Measure_(mathematics)

    Most measures met in practice in analysis (and in many cases also in probability theory) are Radon measures. Radon measures have an alternative definition in terms of linear functionals on the locally convex topological vector space of continuous functions with compact support. This approach is taken by Bourbaki (2004) and a number of other ...

  4. Conversion of units - Wikipedia

    en.wikipedia.org/wiki/Conversion_of_units

    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.

  5. Equivalence of metrics - Wikipedia

    en.wikipedia.org/wiki/Equivalence_of_metrics

    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 ...

  6. Outer measure - Wikipedia

    en.wikipedia.org/wiki/Outer_measure

    An alternative and equivalent definition. [3] ... See also Encyclopedia of Math ... This is the construction used in the definition of Hausdorff measures for a metric ...

  7. Tightness of measures - Wikipedia

    en.wikipedia.org/wiki/Tightness_of_measures

    Another equivalent criterion of the tightness of a collection is sequentially weakly compact. We say the family M {\displaystyle M} of probability measures is sequentially weakly compact if for every sequence { μ n } {\displaystyle \left\{\mu _{n}\right\}} from the family, there is a subsequence of measures that converges weakly to some ...

  8. System of units of measurement - Wikipedia

    en.wikipedia.org/wiki/System_of_units_of_measurement

    A baby bottle that measures in three measurement systems—metric, imperial (UK), and US customary. Metric systems of units have evolved since the adoption of the first well-defined system in France in 1795. During this evolution the use of these systems has spread throughout the world, first to non-English-speaking countries, and then to ...

  9. Glossary of mathematical symbols - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_mathematical...

    That is, whatever A and B are, A ≤ B is equivalent to A < B or A = B. 2. Between two groups, may mean that the first one is a subgroup of the second one. ≥ 1. Means "greater than or equal to". That is, whatever A and B are, A ≥ B is equivalent to A > B or A = B. 2. Between two groups, may mean that the second one is a subgroup of the ...