✦ LIBER ✦

Absolute Continuity and Zero-Sets

✍ Scribed by William D. L. Appling

Publisher: John Wiley and Sons
Year: 1968
Tongue: English
Weight: 349 KB
Volume: 36
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19680360302

No coin nor oath required. For personal study only.

✦ Synopsis

Theorem K. If H i s u reul-valued function on S szcch that j R H ( I ) exists, then

Suppose that each of u, b, c, and d is a nonnegative number and 0 < p < 1.

We see that

This implies that if each of f and g is in U and each of P and F' is a refinement of the subdivision E of the set V of S , then 5 zl? min (f(I), g ( l ) ) 5 zE min (f(I), g ( I ) )

5 z E f (I)" g(l)l-" 5 zE max {f(I), g('))

5 23) max {f (4, g (41 5 f( V ) + 9( v

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