While off-spinner Muralitharan needs five wickets to become Test cricket's most successful bowler, seamer Vaas will become only the third Sri Lankan to play 100 Test matches.
The two impending feats have excited local fans, but Jayawardene was confident his team will not be distracted by what he says are "magnificent achievements that cricketers only dream of.
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"All of us are experienced enough to realise it is a Test series and we really need to play some very good cricket," Jayawardene told reporters after his team's practice session on Friday.
"The records will come but we will also be concerned with what the result will be after three Test matches.
The focus will be to start very well, get at it from the beginning itself and play really positive cricket."
Muralitharan, 35, with 704 wickets in the bag, returns to his home town to cross retired Australian Shane Warne's world mark of 708, a feat Jayawardene said he and the entire team were looking forward to.
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