borel set sentence in Hindi
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- Any measure defined on the Borel sets is called a Borel measure.
- Some authors define a Haar measure on Baire sets rather than Borel sets.
- Note that the boldface hierarchy is just the standard hierarchy of Borel sets.
- Classical descriptive set theory includes the study of regularity properties of Borel sets.
- Each lightface Borel set has infinitely many distinct codes.
- Just beyond the Borel sets in complexity are the analytic sets and coanalytic sets.
- Every Baire set is a Borel set.
- Borel sets and the associated Borel hierarchy also play a fundamental role in descriptive set theory.
- The generalization to Borel sets is more involved, and requires the theory of Suslin sets.
- Although any continuous preimage of a Borel set is Borel, not all analytic sets are Borel sets.
- Although any continuous preimage of a Borel set is Borel, not all analytic sets are Borel sets.
- One way to do this is to define a measure on the Borel sets of the topological space.
- Baire sets avoid some pathological properties of Borel sets on spaces without a countable base for the topology.
- It is not-finite, as not every Borel set is at most a countable union of finite sets.
- For example, all Borel sets of a Polish space have the property of Baire and the perfect set property.
- One common use of the Borel hierarchy is to prove facts about the Borel sets using transfinite induction on rank.
- To denote the number of points of { N } located in some Borel set B, it is sometimes written
- It was shown in 1975 by Donald A . Martin that games whose winning set is a Borel set are determined.
- A code for a lightface Borel set gives complete information about how to recover the set from sets of smaller rank.
- In relation to a Borel set " B " the intensity measure of { N } is defined as:
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