borel set वाक्य
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- In 2010 Calvin Borel set a new record, being the first jockey to win 3 out of 4 consecutive Kentucky Derbys.
- The Borel sets in the following statement refer to the ?-algebra generated by the " open " sets.
- It follows easily from this characterization of propositions in classical systems that the corresponding logic is identical to that of some Borel sets.
- Let the counting measure,, of a Borel set be defined as the number of elements of if is finite, and otherwise.
- The measurable sets on the line are iterated countable unions and intersections of intervals ( called Borel sets ) plus-minus null sets.
- Since every open set is almost open ( the empty set is meager ), it follows that every Borel set is almost open.
- Alternatively, the number of points of \ textstyle { N } located in some Borel set \ textstyle B is often written as:
- In some contexts, Borel sets are defined to be generated by the compact sets of the topological space, rather than the open sets.
- In practice, the use of Baire measures on Baire sets can often be replaced by the use of regular Borel measures on Borel sets.
- Let X be a complete separable metric space and \ mathfrak { B } ( X ) the ?-algebra of its Borel sets.
- The Borel sets in the statement of the theorem also refers to the ?-algebra generated by the " open " sets.
- For subsets of Polish spaces, Borel sets can be characterized as those sets which are the ranges of continuous injective maps defined on Polish spaces.
- It can be proved that for every Borel set contained in, and for every, there exist a closed set and an open set such that
- The code for a lightface Borel set " A " can be used to inductively define a tree whose nodes are labeled by codes.
- For example, it can be shown that an inverse image f ^ {-1 } [ 0 ] is a non-Borel set.
- Alternatively, the number of points of " N " located in some Borel set " B " is often written as:
- The left Haar measure satisfies the inner regularity condition for all ?-finite Borel sets, but may not be inner regular for " all"
- For instance, a "'real-valued measurable function "'is a function for which the preimage of each Borel set is measurable.
- Given a countably additive measure ? on " X ", a measurable set is one that differs from a Borel set by a null set.
- Unfortunately, without the axiom of choice, it is not clear that the "-Borel sets " are " closed under wellordered union.
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