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For a multipartite correlation experiment with an arbitrary number ofsettings and any spectral type of outcomes at each site, we introduce a singlegeneral representation incorporating in a unique manner all Bell-typeinequalities for either correlation functions or joint probabilities that havebeen introduced or will be introduced in the literature. Specifying thisgeneral representation for correlation functions, we prove that the form of anycorrelation Bell-type inequality does not depend on a spectral type of observedoutcomes, in particular, on their numbers at different sites, and is determinedonly by extremal values of outcomes at each site. We also specify the generalform of bounds in Bell-type inequalities on joint probabilities. Our approachto the derivation of Bell-type inequalities is universal, concise and can beapplied to a multipartite correlation experiment with outcomes of any spectraltype, discrete or continuous. We, in particular, prove that, for an N-partitequantum state, possibly, infinite dimensional, admitting the 2x...x2-settingLHV description, the Mermin-Klyshko inequality holds for any two boundedquantum observables per site, not necessarily dichotomic.

Multipartite Bell-type inequalities for arbitrary numbers of settings and outcomes per site