Terms of TOS Definition
Sample Correctly extracted material from the lot, which only originates from a qualified sampling process (“sampling correctness”).
Composite sample Aggregation of several increments – a composite sample constitutes “physical averaging”.
Specimen A ‘sample’ that cannot be documented to be representative.
Increment Correctly delineated, materialised sampling units of the lot. Composite samples result from an increment aggregation process. 
Fragment Smallest separable unit of the lot, e.g. mineral grain, kernel, biological cell etc. that is not affected by the sampling process itself. By naming the smallest unit-of-interest a fragment, TOS allows to treat even the situation in which the sampling process results in fragmentation of (some) of the original units.
Lot Sampling target, e.g. truck load, railroad car, ship’s cargo, batch etc.   Lot refers both to the physical, geometrical form as well as the physic-chemical characteristics of the material being subject to sampling. Lots can be either stationary or dynamic (moving).
Lot dimensionality TOS distinguishes between 0-, 1-, 2- and 3-dimensional lots. A 0-dimensional lot can be manipulated (forcefully mixed, moved etc.) in its entirety without undue efforts. 
Scale Heterogeneity, and counter-acting sampling efficiency, is influential at all scales from increment to lot. Correct sampling is scale-invariant, i.e. the same principles apply to all relevant scales in the sampling pathway.
Heterogeneity Heterogeneity is the prime characterisation of all naturally occurring materials, including industrial lots. Heterogeneity manifests itself at all scales related to sampling for nearly all lot and material types. The only exception is uniform materials1, which however are such rare occurrences that no generalisation w.r.t. general sampling can be made here from.
Sampling correctness Elimination of sampling bias, by correct design, performance and maintenance of the sampling process/equipment. In the event of sampling correctness, only sampling precision remains, which is a much easier issue to control for within specified limits.
Representativeness Representativeness implies both correctness as well as a sufficiently small sampling reproducibility (sampling precision).
1Uniform materials: Materials with a repeated (correct) sampling reproducibility lower than 2% (or lower still, various definitions pertain to different sciences and technology fields). Such materials do only very rarely occur naturally however (exception gasses and infinitely diluted solutions etc.).
Table 1: Fundamental concepts and definitions in Theory of Sampling. See also literature cited immediately above for a more fully developed introduction to TOS and TSP.