:: deftheorem defines is_Lipschitzian_on NFCONT_1:def 9 :
for S, T being RealNormSpace
for X being set
for f being PartFunc of S,T holds
( f is_Lipschitzian_on X iff ( X c= dom f & ex r being Real st
( 0 < r & ( for x1, x2 being Point of S st x1 in X & x2 in X holds
||.((f /. x1) - (f /. x2)).|| <= r * ||.(x1 - x2).|| ) ) ) );