baire set造句

• Some authors define a Haar measure on Baire sets rather than Borel sets.
• Every Baire set is a Borel set.
• Baire sets avoid some pathological properties of Borel sets on spaces without a countable base for the topology.
• There are several inequivalent definitions of Baire sets, but in the most widely used, the Baire sets of a measurable.
• There are several inequivalent definitions of Baire sets, but in the most widely used, the Baire sets of a measurable.
• There are several inequivalent definitions of Baire sets, so correspondingly there are several inequivalent concepts of Baire measure on a topological space.
• In practice, the use of Baire measures on Baire sets can often be replaced by the use of regular Borel measures on Borel sets.
• Baire sets were introduced by, and, who named them after Baire functions, which are in turn named after Ren?Louis Baire.
• For spaces that are not ?-compact the Baire sets under this definition are those under Halmos's definition together with their complements.
• For non-Hausdorff spaces the definitions of Baire sets in terms of continuous functions need not be equivalent to definitions involving G? compact sets.
• For every compact Hausdorff space, every finite Baire measure ( that is, a measure on the ?-algebra of all Baire sets ) is regular.
• Defined Baire sets of a locally compact Hausdorff space to be the elements of the ?-ring generated by the compact " G " ? sets.
• In other words, the ? algebra of Baire sets is the ? algebra " generated " by all compact " G " ? sets.
• The ?-algebra of Borel sets is most popular, but not the only choice ( Baire sets, universally measurable sets etc . are used sometimes ).
• In mathematics, more specifically in measure theory, the "'Baire sets "'form a ?-algebra of a topological space that avoids some of the pathological properties of Borel sets.
• Moreover, some authors add restrictions on the topological space that Baire sets are defined on, and only define Baire sets on spaces that are compact Hausdorff, or locally compact Hausdorff, or ?-compact.
• Moreover, some authors add restrictions on the topological space that Baire sets are defined on, and only define Baire sets on spaces that are compact Hausdorff, or locally compact Hausdorff, or ?-compact.
• There are at least three inequivalent definitions of Baire sets on locally compact Hausdorff spaces, and even more definitions for general topological spaces, though all these definitions are equivalent for locally compact ?-compact Hausdorff spaces.
• In a Cartesian product of uncountably many compact Hausdorff spaces with more than one point, a point is never a Baire set, in spite of the fact that it is closed, and therefore a Borel set.
• Alternatively Baire sets form the smallest ?-algebra such that all continuous functions of compact support are measurable ( at least on locally compact Hausdorff spaces : on general topological spaces these two conditions need not be equivalent ).