§0. Introduction. Few methods are known to construct non Lebesgue-measurable sets of reals: most standard ones start from a well-ordering of R, or from the existence of a non-trivial ultrafilter over ω, and thus need the axiom of choice AC or at least the Boolean Prime Ideal theorem BPI (see [5]). In this paper we present a new way for proving the existence of non-measurable sets using a conven...

Topological measures and quasi-linear functionals generalize linear functionals. We define study deficient topological on locally compact spaces. A measure a space is set function open closed sets which finitely additive sets, inner regular outer sets. Deficient measures. First we investigate positive, negative, total variation of signed that only assumed to be These variations turn out Then ex...

We indicate two problems with the specifications of fairness that are currently used for the verification of non-repudiation and other fair-exchange protocols. The first of these problems is the implicit assumption of perfect information. The second problem is the possible lack of effectiveness. We solve both problems in isolation by giving new definitions of fairness, but leave the combined so...

STUDY OBJECTIVE A number of measures have been developed which attempt to combine a range of variables into a single, more easily understood dimension of "deprivation". These extend from fairly simple additive measures through to those based on more sophisticated statistical techniques. All attempts to simplify a number of variables into a single, summary measure have limitations. This paper co...

purpose: regarding the high prevalence of low back pain in various communities and the need to determine an appropriate treatment plan for these patients, examining their functional limitation and disability level is of utmost importance. in this regard, one of the important indicators is lumbar range of motion. measurement of the range of motion is a common and appropriate method for determini...

Combining ability effects were estimated for different agronomic characters in line × tester crossing program comprising 21 hybrids produced by crossing 7 lines and 3 testers. Parents and hybrids differed significantly for general combining ability (GCA) and specific combining ability (SCA) effects, respectively. The variance due to GCA and SCA showed that gene action was predominantly additive...

In this work we extend the first part of the previous paper [F4] to higher dimensional local fields. We introduce a nontrivial translation invariant measure on the additive group of higher dimensional local fields, and then develop elements of integration and harmonic analysis. We also discuss its relation with several other measure theories. For an n-dimensional local field F a translation inv...