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On the equivalence of the entropic curvature-dimension condition and Bochner’s inequality on metric measure spaces

, 2013
We prove the equivalence of the curvature-dimension bounds of Lott–Sturm–Villani (via entropy and optimal transport) and of Bakry–Émery (via energy and $$\Gamma _2$$Γ2-calculus) in complete generality for infinitesimally Hilbertian metric measure spaces.
Matthias Erbar   +2 more
semanticscholar   +1 more source

Equivalent focal length measurements

SPIE Proceedings, 1999
Converting linear coordinates in the plane of the detector of an astronomical instrument to celestial coordinates involves in principle the equivalent focal length of the instrument. However, most methods in astrometry manage to reduce observations in a global manner without actually measuring a focal length.
Guy E. Artzner   +3 more
openaire   +1 more source

Equivalence-Scale Measurement

2004
This chapter is devoted to a presentation and discussion of the three main approaches to measuring equivalence scales which are the expert approach, the economic approach, and the survey approach. Most attention will be paid to the economic and to the survey approach since both are applied in this thesis.
openaire   +1 more source

Equivalence in Measurement

2001
This volume highlights research and conceptual insights into one of the most basic, and yet, perplexing research issues in management-handling and assessing the comparability of our measurement devices across groups and measures. One of the most consistently difficult concerns in management research over the past three decades has been trying to ...
openaire   +1 more source

On Non-Equivalence of Equivalence Range Measures

Perceptual and Motor Skills, 1973
Measures of equivalence range were intercorrelated in three studies in order to determine the equivalence of the measures and constructs from which the measures were derived. In none of the studies were the intercorrelations significant. Thus, the ability to generalize from results obtained with any one measure is limited, and the meaning of the ...
openaire   +1 more source

Strongly equivalent invariant measures

Mathematical Proceedings of the Cambridge Philosophical Society, 1980
AbstractTwo measures are strongly equivalent if they have the same sets of zero measure and the same sets of infinite measure. Given a group G of strongly non-singular measurable transformations of a non-atomic positive measure space (X, β, p), if G is amenable, then a necessary and sufficient condition for there to be a G-invariant positive measure on
openaire   +2 more sources

The Theory of Countable Borel Equivalence Relations


The theory of definable equivalence relations has been a vibrant area of research in descriptive set theory for the past three decades. It serves as a foundation of a theory of complexity of classification problems in mathematics and is further motivated
A. Kechris
semanticscholar   +1 more source

Teach Measurement Equivalencies Simply

Academic Therapy, 1984
In this step-by-step approach, children with learning disabilities can learn basic measurement equivalencies they they will need for mathematical and vocational objectives.
openaire   +1 more source

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