The study of property testing was initiated by Rubinfeld and Sudan [RS96] and significantly expanded by Goldreich, Goldwasser, and Ron [GGR98]; the stricter notion of local testability was introduced (in the context of error-correcting codes) by Friedl and Sudan [FS95]. The first local tester for dictatorship was given by Bellare, Goldreich, and Sudan [BGS95,BGS98] (as [...]

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Ohad Klein: In lemma 46 (48) - should it be $i \not \in J'_x$? (In its ...Ohad Klein: Another one - is the symbol "union" is redundant in 37b,c?Ohad Klein: I might be misunderstanding 37b. Suppose k=n=1. Then $E[f^q]...Ohad Klein: I might be wrong, but in ex. 9.31 (i.e. remark 9.29), I trie...Ohad Klein: sorry, my bad, again!Ohad Klein: In 23, is it $q \leq 2+2\epsilon$?Ohad Klein: ctrl+f: Paresval.