Probability Spaces

2021 ◽  
pp. 147-153
Author(s):  
James Davidson
Keyword(s):  
Conditional Probability ◽  
General Context ◽  
Probability Measures ◽  
Product Spaces ◽  
Probability Spaces ◽  
Product Measures

This chapter defines probability measures and probability spaces in a general context, as a case of the concepts introduced in Chapter 3. The axioms of probability are explained, and the important concepts of conditional probability and independence are introduced and linked to the role of product spaces and product measures.

A Comparison of Methods for Constructing Probability Measures on Infinite Product Spaces

1987 ◽  
Vol 30 (3) ◽  
pp. 282-285 ◽  
Author(s):  
Charles W. Lamb
Keyword(s):  
Probability Measure ◽  
Conditional Probability ◽  
Product Space ◽  
Infinite Product ◽  
Probability Measures ◽  
Classical Theorem ◽  
Comparison Of Methods ◽  
Product Spaces ◽  
Probability Functions ◽  
Finite Dimensional

AbstractThe construction, from a consistent family of finite dimensional probability measures, of a probability measure on a product space when the marginal measures are perfect is shown to follow from a classical theorem due to Ionescu Tulcea and known results on the existence of regular conditional probability functions.

Boundary layer over a blunt body at low incidence with circumferential reversed flow

1975 ◽  
Vol 72 (1) ◽  
pp. 49-65 ◽  
Author(s):  
K. C. Wang
Keyword(s):  
Boundary Layer ◽  
Skin Friction ◽  
Blunt Body ◽  
Three Dimensional ◽  
Prolate Spheroid ◽  
Three Dimensions ◽  
General Context ◽  
Reversed Flow ◽  
Low Incidence

This paper investigates the three-dimensional laminar boundary layer over a blunt body (a prolate spheroid) at low incidence and with reversed flow. Results reflecting the general characteristics of such a problem are presented. More significant are the features relating to the circumferential flow reversal. Some of these features confirm our early hypotheses concerning the existence of a reversed region ahead of separation and the role of the zero-cfθ line in the general context of separation in three dimensions. Other features are unexpected, including the distribution of cfμ and the shape of the separation line. Here cfθ and cfμ denote, respectively, the circumferential and meridional components of the skin friction.

scholarly journals Construction of Fuzzy Measures over Product Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1605 ◽  
Author(s):  
Fernando Reche ◽  
María Morales ◽  
Antonio Salmerón
Keyword(s):  
Product Space ◽  
Fuzzy Measure ◽  
Product Measure ◽  
Product Spaces ◽  
Joint Function ◽  
Single Product ◽  
Fuzzy Measures ◽  
Statistical Indices ◽  
Product Measures ◽  
Definition Of

In this paper, we study the problem of constructing a fuzzy measure over a product space when fuzzy measures over the marginal spaces are available. We propose a definition of independence of fuzzy measures and introduce different ways of constructing product measures, analyzing their properties. We derive bounds for the measure on the product space and show that it is possible to construct a single product measure when the marginal measures are capacities of order 2. We also study the combination of real functions over the marginal spaces in order to produce a joint function over the product space, compatible with the concept of marginalization, paving the way for the definition of statistical indices based on fuzzy measures.

scholarly journals Religious experience and the probability of theism: comments on Swinburne

2017 ◽  
Vol 53 (3) ◽  
pp. 353-370 ◽  
Author(s):  
CHRISTOPH JÄGER
Keyword(s):  
Conditional Probability ◽  
Religious Experience ◽  
Prior Probability ◽  
Rational Belief ◽  
Religious Experiences ◽  
Phenomenal Conservatism ◽  
Rival Hypothesis

AbstractI discuss the role of religious experience in Richard Swinburne's probabilistic case for theism. Swinburne draws on his principle of credulity to argue that, if in addition to other evidence we consider that many people have theistic religious experiences, theism comes out as more probable than not. However, on many plausible probability assignments for the relevant non-experiential evidence, the conditional probability of theism already converges towards 1. Moreover, an argument analogous to a general Bayesian argument against phenomenal conservatism suggests that, after we take account of evidence from religious experience, the probability of theism cannot be greater than the prior probability that the best rival hypothesis is false. I conclude that these observations are compatible with what Swinburne would call ‘weak rational belief’ in theism and that such weak belief can be strong enough for rational faith.

Multivariate monotone likelihood ratio and uniform conditional stochastic order

1982 ◽  
Vol 19 (3) ◽  
pp. 695-701 ◽  
Author(s):  
Ward Whitt
Keyword(s):  
Conditional Probability ◽  
Likelihood Ratio ◽  
Probability Distributions ◽  
Stochastic Order ◽  
Total Positivity ◽  
Probability Measures ◽  
Monotone Likelihood Ratio ◽  
Fkg Inequality ◽  
The Fkg Inequality

Karlin and Rinott (1980) introduced and investigated concepts of multivariate total positivity (TP2) and multivariate monotone likelihood ratio (MLR) for probability measures on Rn These TP and MLR concepts are intimately related to supermodularity as discussed in Topkis (1968), (1978) and the FKG inequality of Fortuin, Kasteleyn and Ginibre (1971). This note points out connections between these concepts and uniform conditional stochastic order (ucso) as defined in Whitt (1980). ucso holds for two probability distributions if there is ordinary stochastic order for the corresponding conditional probability distributions obtained by conditioning on subsets from a specified class. The appropriate subsets to condition on for ucso appear to be the sublattices of Rn. Then MLR implies ucso, with the two orderings being equivalent when at least one of the probability measures is TP2.

Toward a Modified Structural Syllabus

1982 ◽  
Vol 5 (1) ◽  
pp. 34-51 ◽  
Author(s):  
Albert Valdman
Keyword(s):  
Foreign Language ◽  
Communicative Competence ◽  
Target Language ◽  
General Context ◽  
Teaching Materials ◽  
Rhetorical Devices ◽  
Functional Orientation ◽  
Linguistic Means

This paper argues for an integration of the notion of communicative competence in the elaboration of syllabuses and the preparation of teaching materials for beginning and intermediate generalforeign languagecourses. A distinction is made between such courses and the teaching of English as a medium of wider communication on an international basis. In FL instruction, as opposed to the teaching of a MWC, metalinguistic, epilinguistic, or cultural objectives may be more highly valued than the use of language for daily communication. In addition, the general context of FL instruction precludes the authentic use of the target language in the classroom, a prerequisite for the attainment of communicative competence. The integration of the notion of communive competence in FL instruction, including the inclusion of notions and functions, involves the grafting of these last mentioned considerations onto a structural-situational-functional base. That base would be modified by moving in five directions: (1) adopting a functional orientation, i.e., providing learners with linguistic means to express notions and functions rather than the teaching of structures for their own sake; (2) focus on semantic notions; (3) cyclical progression; (4) aiming for discursive authenticity by identifying rhetorical devices) providing stylistic manoeuver by the recognition of the role of variants.

Sign in / Sign up

Export Citation Format

Share Document