Integrationstheorie

Integrationstheorie is a term used in both mathematics and the social sciences to describe theories about combining parts into a whole, but in each field it refers to different concepts and methods.

In mathematics, Integrationstheorie denotes the branch of analysis concerned with defining and evaluating integrals. Classical formulations include the Riemann integral and the Lebesgue integral, with measure theory providing a unifying foundation. Generalizations extend to vector-valued functions through Bochner and Pettis integration and to broader function classes via approaches such as Henstock–Kurzweil integration. Key ideas include linearity, additivity, and convergence theorems (for example, monotone and dominated convergence), which ensure the robustness of integration under limiting processes. In probability theory, integration plays a central role through expectations and distributional properties defined as integrals with respect to probability measures.

In the social sciences, Integrationstheorie refers to theories about how individuals oder groups become part of a society. Central questions concern inclusion, belonging, social cohesion, and the paths by which migrants, minorities, or marginalized groups participate in economic, political, and cultural life. Dominant theoretical approaches include assimilationist models, multiculturalist or intercultural perspectives, and segmented or stratified integration theories. Mechanisms and factors emphasized include language acquisition, education, labor market access, social networks, discrimination, and institutions such as welfare, housing, and civic language programs. Indicators used to assess integration encompass employment and education outcomes, language proficiency, civic participation, and social contacts across groups. Policy debates often contrast integration through civic assimilation with recognition of plural identities and equal rights.

The term thus covers distinct but conceptually related ideas: rigorous mathematical methods for aggregating quantities, and social science models of how societies absorb and incorporate diverse populations.