"limits of infinity" exist:

 1') f(s ,) = llm f(s',t')
 s'+ns


 2') f(s ,-) = llm f(s',t')
 t'+ts


 3') f(=,t ) = lim f(s',t')
 t'44t


 4') f(m,t ) = lim f(s',t'), and especially
 t '++t


 5') f(m) = lim f(s',t') exists.
 s',t't~


b) If, moreover, f is right continuous, then the one-sided limits

along the vertical and horizontal paths f(s,-), f(-t) are equal to the

following.

 i) lim f(,t) = lim f(s,') = f(s+,t+) (right limits)
 s'4~s t'++t

 ii) lim f(-,t) = f(s-,t+), and
 s'tts

 lim f(-,t) = f(W,t+) if Ifl is bounded.
 s 't

 iii) lim f(s,-) = f(s+,t-), and
 t'tt

 lim f(s,-) = f(s+,-) if Ifl is bounded.
 t'+





Remarks. 1) Here f is defined on R2: if we wish to use an f defined

also on the "boundary at infinity," the above limits will be denoted

with the symbol -- in place of ".