= p-adic measure
{c}
{title2=$\mu:C(G,I)\to I$}
For a <profinite group> $G$ and a complete <discrete valuation ring> $I$ with a continuous $\mathbb Z_p$-algebra structure, an $I$-valued measure is a bounded $I$-linear functional on continuous $I$-valued functions, with the <uniform norm>. Equivalently it assigns finitely additive values in $I$ to <clopen sets>. <Locally constant functions> are uniformly dense, so <integration> extends uniquely from finite sums. <Countable additivity> in the usual real-measure sense is not imposed. The coefficient ring may have infinite <residue field> and need not be compact.
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