Let u be a δ-subharmonic function with associated measure µ, and let v be a superharmonic function with associated measure ν, on an open set E. For any closed ball B(x,r), of centre x and radius r, contained in E, let M(u, x, r) denote the mean value of u over the surface of the ball. We prove that the upper and lower limits as s, t → 0 with 0 <s<t of the quotient (M(u, x,s)−M(u, x,t))/(M(v,x,s)−M(v,x,t)), lie between the upper and lower limits as r → 0+ of the quotient µ(B(x,r))/ν(B(x,r)). This enables us to use some well-known measure-theoretic results to prove new variants and generalizations of several theorems about δ-subharmonic functions.
Implicit causality (IC) verbs influence the pronoun ambiguity resolution by directing the speakers’ (readers’ or listeners’) attention to the referent that is likely to be the cause of the event or state. Although IC bias is considered universal, there are cross-linguistic differences in its direction and strength. Previous studies have attempted to build large datasets of IC verbs, but very few Slavic languages have been investigated. In this experimental study, we examined the direction and strength of IC bias in Croatian, an understudied Slavic language in this regard, and compared it with IC bias observed in English. After selecting 137 verbs and classifying them according to thematic roles (agent-patient, agent-evocator, stimulus-experiencer, experiencer-stimulus), 86 participants were asked to complete sentence fragments containing these verbs. The study was conducted under the semantic structure account. Our results show that most Croatian verbs followed the predicted direction, which is consistent with findings suggesting that the direction of IC bias is relatively generalizable across languages. We also detected cross-linguistic variability in the strength of IC bias, especially in stimulus-experiencer verbs. This is consistent with studies showing that the strength of IC bias can vary across languages. Implications for theoretical and methodological approaches are discussed. and Implicitnouzročni glagoli utječu na razdvosmislenje upućivanja zamjenicom usmjeravajući govornikovu (čitateljevu ili slušateljevu) pozornost na referent koji je vjerojatniji uzrok događaja ili stanja. Iako se implicitnouzročna pristranost smatra univerzalnom, pronađene su međujezične razlike u smjeru i jačini glagolske pristranosti. U prijašnjim se istraživanjima težilo stvaranju velikih baza implicitnouzročnih glagola, no ta je jezična pojava nedovoljno istražena u slavenskim jezicima. Cilj ovoga eksperimentalnoga istraživanja bio je ispitati smjer i jačinu pristranosti implicitnouzročnih glagola u hrvatskome, koji je slavenski jezik i u kojem je ta pojava slabo istražena, te dobivene podatke usporediti s podatcima u engleskom jeziku. Izabrano je 137 glagola koji su razvrstani prema semantičkim ulogama (agens – pacijens, agens – pobuđivač, poticajnik – doživljavač, doživljavač – poticajnik). Ukupno je 86 sudionika dovršavalo rečenice s tim glagolima. Istraživanje je provedeno u okviru pristupa značenjske strukture. Rezultati pokazuju da većina hrvatskih glagola pokazuje predviđeni smjer pristranosti, što je u skladu s istraživanjima koja upućuju na to da je smjer implicitnouzročne pristranosti sličan u različitim jezicima. S druge strane, pronađene su međujezične razlike u snazi glagolske pristranosti, ponajprije u kategoriji poticajnik – doživljavač. Taj je rezultat u skladu s istraživanjima koja pokazuju da se jačina implicitnouzročne pristranosti može razlikovati među jezicima. U radu se raspravlja o teorijskim i metodološkim implikacijama.