:: deftheorem DefYvol defines Y-vol MEASUR11:def 13 :
for X1, X2 being non empty set
for S1 being SigmaField of X1
for S2 being SigmaField of X2
for M2 being sigma_Measure of S2
for E being Element of sigma (measurable_rectangles (S1,S2)) st M2 is sigma_finite holds
for b₇ being nonnegative Function of X1,ExtREAL holds
( b₇ = Y-vol (E,M2) iff ( ( for x being Element of X1 holds b₇ . x = M2 . (Measurable-X-section (E,x)) ) & ( for V being Element of S1 holds b₇ is V -measurable ) ) );