منابع مشابه
Ideals without CCC
Let I be an ideal of subsets of a Polish space X, containing all singletons and possessing a Borel basis. Assuming that I does not satisfy ccc, we consider the following conditions (B), (M) and (D). Condition (B) states that there is a disjoint family F ⊆ P (X) of size c, consisting of Borel sets which are not in I . Condition (M) states that there is a Borel function f : X → X with f[{x}] / ∈ ...
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We prove a strong version of a theorem of Balcerzak-RoslanowskiShelah by showing, in ZFC, that there exists a simply definable Borel σ-ideal for which both the ccc and property (M) fail. The proof involves Polish group actions. Definition. A Borel ideal is an ideal I on a Polish space X with the following property: for all A ∈ I, there exists a Borel subset B of X such that A ⊂ B and B ∈ I. We ...
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Here A is a square matrix of order n, whose elements are given real numbers ai3' with a determinant d(A)9 0] x and b denote column vectors, and the components of b are given real numbers. (Complex numbers would offer no essential difficulty.) It is desired to calculate the components of the unique solution x = A~b; here A~ is the inverse of A. Such problems arise in the most diverse branches of...
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We present a parameter estimation technique based on performing joint measurements of a weak interaction away from the weak-value-amplification approximation. Two detectors are used to collect full statistics of the correlations between two weakly entangled degrees of freedom. Without discarding of data, the protocol resembles the anomalous amplification of an imaginary-weak-value-like response...
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Over the last few decades, philosophy has gained an increasingly bad reputation among working scientists. Prominent researchers have suggested, in various forms and degrees of mockery, that philosophy has little or nothing positive to contribute to science. This essay provides a response to these allegations. We begin by examining, and ultimately questioning, an influential argument purporting ...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1994
ISSN: 0166-8641
DOI: 10.1016/0166-8641(94)90040-x