English
The symbol ∏' i, f i denotes the unconditional product of f with respect to a summation filter, existing if possible, otherwise equal to 1.
Русский
Символ ∏' i, f i обозначает неопосредованный произведение f по отношению к суммирующему фильтру: существует — есть произведение; не существует — единица.
LaTeX
$$$ \text{tprod} = \text{unconditional product with respect to } L\ (exists \text{ ifHasProd } f a L, \text{ else } 1) $$$
Lean4
/-- `∏' i, f i` is the unconditional product of `f`, if it exists, or 1 otherwise. ]
More generally, if `L` is a `SummationFilter`, `∏'[L] i, f i` is the product of `f` with respect to
`L` if it exists, and `1` otherwise.
(Note that even if the unconditional product exists, it might not be unique if the topology is not
separated. When the multiplicative support of `f` is finite, we make the most reasonable choice,
to use the product over the multiplicative support. Otherwise, we choose arbitrarily an `a`
satisfying `HasProd f a`. Similar remarks apply to more general summation filters.) -/
noncomputable def tprod :=
val_proj @wrapped✝.{}
