Product integration of measures and applications

Some Applications of Strong Product

Let G and H be graphs. The strong product GH of graphs G and H is the graph with vertex set V(G)V(H) and u=(u1, v1) is adjacent with v= (u2, v2) whenever (v1 = v2 and u1 is adjacent with u2) or (u1 = u2 and v1 is adjacent with v2) or (u1 is adjacent with u2 and v1 is adjacent with v2). In this paper, we first collect the earlier results about strong product and then we present applications of ...

Research on product characteristics: models, applications, and measures

SOME SIMILARITY MEASURES FOR PICTURE FUZZY SETS AND THEIR APPLICATIONS

In this work, we shall present some novel process to measure the similarity between picture fuzzy sets. Firstly, we adopt the concept of intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets and picture fuzzy sets. Secondly, we develop some similarity measures between picture fuzzy sets, such as, cosine similarity measure, weighted cosine similarity measure, set-theoretic similar...

Product Integration

This is a brief survey of product-integration for biostatisticians. 1 Product-Integration Product-integration was introduced more than 110 years ago by the Italian mathematician Vito Volterra, as a tool in the solution of a certain class of differential equations. It was studied intensively by mathematicians for half a century, but finally the subject became unfashionable and lapsed into obscur...

Image Measures of Infinite Product Measures and Generalized Bernoulli Convolutions

We examine measure preserving mappings f acting from a probability space (Ω, F, μ) into a probability space (Ω, F , μ) , where μ = μ(f−1). Conditions on f , under which f preserves the relations ”to be singular” and ”to be absolutely continuous” between measures defined on (Ω, F ) and corresponding image measures, are investigated. We apply the results to investigate the distribution of the ran...