Radon-Nikodym theorem in signed Loeb space

Abstract

This paper gives the Radon-Nikodym theorem in signed Loeb space under 1 ℵ -saturated nonstandard model. First, the nonstandard characterization of absolute continuity is discussed, on which Radon-Nikodym theorem in signed Loeb space is obtained.Then, some facts about a finite signed Loeb measure and its variation are shown.

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“…Mullite (Al 6 Si 2 O 13 ) and its composites have been attracted much attention because of their outstanding properties such as high melting point and strength, low thermal conductivity, good creep and thermal shock resistance, and regarded as promising engineering materials for the high temperature applications [1][2][3]. Recently, mullite [4][5][6][7][8][9] and its composites such as mullitecorundum (Al 2 O 3 ) [10] and mullite-zirconia (ZrO 2 ) [11], have been synthesized from fly ash by reaction sintering method, which can not only reduce the production cost of mullite, but also provide a new route of high value-added-value utilization of fly ash.…”

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“…The finite element model is built by simplifying appropriately the original model, selecting the same element type and physical attribute for the four models. All models of single span area are 4×4m 2 , the height of single-level is 3m, the whole model is a 4-spans 3-story of beam-column-plate frame structure. In order to guarantee get exactly the same dynamic coefficient while the total quality of model 1 is 95.2% from the last three.…”